An exponential function showing the relationship between y and t is:
y(t) = 1500(e)^(-0.0425t)
How to write exponential models?The general form of expression of an exponential growth function is:
y = P(e)^(rt)
where;
y is the Amount you want the account/price/population/etc. to equal
P is the principal, or the amount you start with.
e is a specific irrational number approximately 2.718.
We are given:
In 2004, a forest covered an area of 1500 km². Thus:
y(0) = 1500 km²
r = -4.25% = -0.0425
y(t) = P(e)^(rt)
Thus:
A = y(0) = 1500
Thus:
y(t) = 1500(e)^(-0.0425t)
Read more about Exponential Models at: https://brainly.com/question/2456547
#SPJ1
Which ordered pair in the form (x, y) is a solution of this equation?
x + 6y = 9
Answer:
there is (0,1.5) and (9,0)
Step-by-step explanation:
there is my prrof that this is the answer
The school cafeteria sells three different types of sandwiches: chicken, turkey, and roast beef.
Chicken sandwiches sell for $3, turkey sandwiches sell for $3.50, and roast beef sandwiches sell for $4. The cafeteria makes 500 sandwiches in total, and, if all sandwiches are sold, the cafeteria will take in $1730. If the cafeteria makes the same number of chicken sandwiches as it does turkey sandwiches, how many of each type of sandwich does the school make? Show your work using any method you prefer.
By using a system οf equatiοns, the schοοl makes 180 chicken sandwiches, 180 turkey sandwiches, and 140 rοast beef sandwiches.
What is a system οf equatiοns?A system οf equatiοns is a set οf twο οr mοre equatiοns that need tο be sοlved tοgether tο find the values οf the variables that satisfy all οf the equatiοns.
Let's use a system οf equatiοns tο sοlve the prοblem.
Let c be the number οf chicken sandwiches sοld, t be the number οf turkey sandwiches sοld, and r be the number οf rοast beef sandwiches sοld.
Frοm the prοblem, we knοw that:
c + t + r = 500 (the tοtal number οf sandwiches sοld is 500)
3c + 3.5t + 4r = 1730 (the tοtal revenue frοm selling all sandwiches is $1730)
We alsο knοw that the cafeteria makes the same number οf chicken sandwiches as it dοes turkey sandwiches, sο: c = t
Nοw we can substitute c fοr t in the first twο equatiοns:
c + c + r = 500
3c + 3.5c + 4r = 1730
Simplifying these equatiοns, we get:
2c + r = 500
6.5c + 4r = 1730
We can sοlve fοr r in the first equatiοn:
r = 500 - 2c
Substituting this intο the secοnd equatiοn and sοlving fοr c, we get:
6.5c + 4(500 - 2c) = 1730
6.5c + 2000 - 8c = 1730
-1.5c = -270
c = 180
Sο the cafeteria sells 180 chicken sandwiches and 180 turkey sandwiches (since c = t). We can find the number οf rοast beef sandwiches by substituting c and t intο οne οf the οriginal equatiοns:
c + t + r = 500
180 + 180 + r = 500
r = 140
Therefοre, the schοοl makes 180 chicken sandwiches, 180 turkey sandwiches, and 140 rοast beef sandwiches.
To learn more about system of equations visit:
brainly.com/question/21620502
#SPJ1
Simplify the given expression, and most importantly show the steps, please.
Answer:
(3 sqrt(2))/2
Step-by-step explanation:
Simplify the following:
6/sqrt(8)
Rationalize the denominator. 6/sqrt(8) = 6/sqrt(8)×(8^(1 - 1/2))/(8^(1 - 1/2)) = (6×8^(1 - 1/2))/8:
(6×8^(1 - 1/2))/8
The gcd of 6 and 8 is 2, so (6×8^(1 - 1/2))/8 = ((2×3) 2 sqrt(2))/(2×4) = 2/2×(3×2 sqrt(2))/4 = (3×2 sqrt(2))/4:
(3×2 sqrt(2))/4
2/4 = 2/(2×2) = 1/2:
Answer: (3 sqrt(2))/2
Given:-
6/√8 .To Do :-
To simplify the given expression.Solution:-
We have ;
[tex]\implies \dfrac{6}{\sqrt8} \\[/tex]
We can write 8 as 2³ . So ,
[tex]\implies \dfrac{6}{\sqrt{2^3}} \\[/tex]
[tex]\implies \dfrac{6}{2\sqrt2} \\[/tex]
[tex]\implies \dfrac{3}{\sqrt2} \\[/tex]
Rationalize the denominator by multiplying numerator and denominator by √2 .
[tex]\implies \dfrac{3\sqrt2}{\sqrt2.\sqrt2} \\[/tex]
[tex]\implies\boxed{ \dfrac{3\sqrt2}{2}} \\[/tex]
This is given required answer.
and we are done!
The function f(x) = 223 - 6a? - 144x + 7 is increasing on the interval
(-00, A) U (B, co) and decreasing on the interval (A, B).
A =
and B =
f is concave up on (C, ∞) and concave down on (-00, C).
C =
The function f(x) = 223 - 6a? - 144x + 7 is increasing on the interval (-00, A) U (B, co)and on the interval (-00, B), the function is decreasing.
What is function?Function in mathematics is a relation or mapping between input and output values. It describes a relationship in which each input value has a single corresponding output value. Functions are an essential part of mathematics, and they are used to model real-world situations. They are also used to solve equations, graph functions, and find the area of a region.
A function is increasing if its rate of change is positive; that is, the function is always getting larger as the independent variable (in this case, x) increases. Conversely, a function is decreasing if its rate of change is negative; that is, the function is always getting smaller as the independent variable increases.
The function f(x) = 223 - 6a? - 144x + 7 is increasing on the interval (-00, A) U (B, co). This means that the rate of change of the function is positive on the specified interval. That is, as x increases within the interval, the value of the function will also increase.
The value of A is the point at which the function changes from increasing to decreasing. That is, on the interval (-00, A), the function is increasing, but on the interval (A, B), the function is decreasing. The value of A can be found by setting the first derivative of the function (the rate of change) equal to 0.
The value of B is the point at which the function changes from decreasing to increasing. That is, on the interval (B, ∞), the function is increasing, but on the interval (-00, B), the function is decreasing. The value of B can be found by setting the first derivative of the function equal to 0.
The value of C is the point at which the function changes from concave up to concave down. That is, on the interval (C, ∞), the function is concave up, but on the interval (-00, C), the function is concave down. The value of C can be found by setting the second derivative of the function equal to 0.
For more questions related to derivative,
https://brainly.com/question/23819325
#SPJ1
Nathan deposits $170 into a savings account that pays 2.25% simple interest annually. If Nathan makes no deposits or withdrawals, how much money will he have in his savings account after 2 years?
Answer:
SI=P*R*T/100
SI=270*2.25*2/100
SI=7.65
TOTAL AMOUNT=7.65+170=177.65
I will mark you brainiest!
A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class passed the first test. What percent of those who passed the first test also passed the second test? How would one find the answer to this model?
A) 0.25 divided by 0.67
B) 0.67 divided by 0.42
C) 0.42 divided by 0.67
D) 0.25 divided by 0.42
Answer:
D) 0.25 divided by 0.42.
Step-by-step explanation:
The answer can be found using the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
Let A be the event of passing the first test and B be the event of passing the second test. We know that:
P(A and B) = 25%
P(A) = 42%
To find P(B|A), we need to divide P(A and B) by P(A):
P(B|A) = P(A and B) / P(A) = 0.25 / 0.42
So the answer is D) 0.25 divided by 0.42.
The product of 4 and a number is 3 less than the number. What is the number?
Answer:
2
Step-by-step explanation:
Approximate the mean for following GFDT.
Data Frequency
50 - 54 1
55 - 59 1
60 - 64 4
65 - 69 3
70 - 74 8
75 - 79 10
80 - 84 15
85 - 89 22
90 - 94 11
mean =
The mean for the grouped frequency data-set given in this problem is as follows:
80.8.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.
The number of observations in the data-set is given as follows:
1 + 1 + 4 + 3 + 8 + 10 + 15 + 22 + 11 = 75.
We are given a frequency distribution, hence for each interval we take the midpoint, and thus the sum of the values is given as follows:
S = 1 x (52 + 57) + 4 x 62 + 3 x 67 + 8 x 72 + 10 x 77 + 15 x 82 + 22 x 87 + 11 x 92
S = 6060.
Hence the mean is given as follows:
6060/75 = 80.8.
More can be learned about the mean of a data-set at brainly.com/question/1156334
#SPJ1
i need help white this one too
The value of x and y in the equation are 1 and -4 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . Example of Simultaneous equation is ;
3x + 2 = y equation 1
5x +3 = 2y equation 2
Simultaneous equations can be solved either by elimination or substitution methods.
y = -7x +3 ( equation 1)
y = -x-3 (equation 2)
subtract equation 1 from 2
-x -(-7) -3-3 = 0
-x+7 -6 = 0
x = 7-6
x = 1
substitute 1 for x in equation 1
y = -7(1) +3
y = -7+3
y = -4
therefore the value of x and y are 1 and -4 respectively
learn more about Simultaneous equation from
https://brainly.com/question/148035
#SPJ1
1.Amy invested £200 into a bank account with 10% simple interest per year. How much money will she have in her account after 2 years?
Answer:
Amy will have £240 in her account.
Step-by-step explanation:
To calculate the amount of money Amy will have in her account after 2 years, we can use the formula:
A = P(1 + rt)
Where:
A = the total amount of money in the account after 2 years
P = the principal (the initial amount of money invested)
r = the interest rate (as a decimal)
t = the time in years
In this case, Amy invested £200 at an interest rate of 10% per year for 2 years. We can plug in these values into the formula and solve for A:
A = 200(1 + 0.1 × 2)
A = 200(1.2)
A = £240
Therefore, after 2 years, Amy will have £240 in her account.
Given ∠=m angle , j m l , equals 80 and ∠=,m angle , k m l , equals 33 comma what is ∠?
The measurement for angle m ∠JMK is obtained as 47°.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The measure of angle JML is given as = 80°.
The measure of angle KML is given as = 33°.
In the image it can be seen that on adding angles - ∠KML and ∠JMK we obtain the angle ∠JML.
This can be represented in the equation form as -
∠JML = ∠KML + ∠JMK
Substitute the values in the equation -
80° = 33° + ∠JMK
Simplify the equation given -
∠JMK = 80° - 33°
∠JMK = 47°
Therefore, the angle JMK measures 47°.
To learn more about angle from the given link
https://brainly.com/question/2046046
#SPJ1
The scatter plot shows prize money, in thousands of dollars, for a contest over eight consecutive years.
Predict the amount of prize money in year 10 of the contest.
A) $11,790
B) $20,340
C) $35,200
D) $45,900
The predicted prize money in year 10 of the contest is $11,790 for the given Scatter plot.
What is a Scatter plot?A set of dots plotted on a horizontal and vertical axis is called as a scatter plot.
We have to find the equation of linear regression using a calculator,
To find the equation, we need to put the entire set of points (x, y) given by the scatter plot in the calculator.
From the scatter plot, points are approximated as follows:
(1, 9.5), (2, 9), (3, 7), (4, 10), (5, 11), (6,10), and (7,10.5).
With the help of a calculator, the amount of prize money in year x of the contest is given by:
P(x) = 0.32143x + 8.28571
To find the predicted amount in year 10, we have to find the numeric value when x = 10,
Hence, P (10) = 0.32143 (10) + 8.28571 = $11,500.
The closest option here is $11,790, which is different from $11,500 because coordinates of points are approximated from scatter plot and not exact.
To learn more about Scatter plot visit:
https://brainly.com/question/6592115
#SPJ1
can someone help me? please
3. a. A solution or feasible region, is the triangular region in the graph of the inequality, with vertices (0.7, -3.35), (8, -7), (8, -25.25)
Please find attached the graph of the feasible region of the inequality, created with MS Excel
b. The feasible region in the graph of the inequality indicates that the inequality remains true for the coordinates of points within the feasible region
What is an inequality?An inequality is an unequal comparison between values or expressions using inequality symbols such as <, >, ≤, and ≥.
3. The system of inequalities are presented as follows;
4·x + 8·y ≤ -24
-12·x - 4·y < 5
a. Making y the subject of the above inequalities, we get;
4·x + 8·y ≤ -24
y ≤ (-24 - 4·x) ÷ 8 = -3 - 0.5·x
y ≤ -3 - 0.5·x...(1)
-12·x - 4·y < 5
-4·y < 5 + 12·x
y > -1.25 - 3·x...(2)
The solution point is therefore;
-3 - 0.5·x = -1.25 - 3·x
2.5·x = 1.75
x = 1.75/2.5 = 0.7
The x-value of the solution point is therefore the point x = 0.7
y > -1.25 - 3 × 0.7 = -3.35
y > -3.35
The y-value of the solution point is the point y > -3.35
The solution point is therefore the point slightly to the right of the point (0.7, -3.35)
b. The solution space is the triangular region bounded by the points, (0.7, -3.35), (8, -7), and (8, -25.25)
A possible solution obtained from the graph is therefore, the point (6, -10), plugging in the values in the inequalities, we get;
When x = 6
y ≤ -3 - 0.5·x...(1)
y ≤ -3 - 0.5 × 6 = -6
The y-value at the point x = 6 is -10 ≤ -6, which satisfies the first inequality
The second inequality, indicates that we get;
y > -1.25 - 3·x
y > -1.25 - 3 × 6 = -19.25
The y-value at the selected point x = 6 is -10 > -19.25, which satisfies the second inequality
Therefore; The inequality is true at a specified point in the solution space as indicated from the graph
Learn more on inequalities here: https://brainly.com/question/27590365
#SPJ1
Question 12
Using the equations Soda = 12.5-0.2475t and Water=8.2+0.56t, if sales of
bottled water continue to increase at this rate and sales of carbonated soft drinks
continue to decline, during what year will the amount sold be the same?
I don't know
You answered 7 out of 11 correctly. Asking up to 12.
2 attempts
The sales of bottled water and carbonated soft drinks will be the same in the year 2028 (in 5.323 years).
How to find the amount sold will be sameTo find the year when the sales of soda and water will be equal, we need to solve the equation:
Soda = Water
12.5 - 0.2475t = 8.2 + 0.56t
where
t = time
collecting like terms
12.5 - 8.2 = 0.2475t + 0.56t
4.3 = 0.8075t
Then we can solve for t by dividing both sides by 0.8075:
t ≈ 5.323
If t is in years, this tells us that the sales of soda and water will be equal in approximately 5.323 years.
To find the year when this will happen, we need to add 5.323 to the current year.
Assuming the current year is 2023, we get:
2023 + 5.323 ≈ 2028.323
Learn more about equation at:
https://brainly.com/question/22688504
#SPJ1
If p varies inversely with q and p=2 when q=1 , find the equation that relates p and q.
Answer: If p varies inversely with q, it means that their product is a constant value, which we can represent as k. That is:
p*q = k
We can solve for k using the given values:
p = 2 when q = 1
2 * 1 = k
k = 2
Now we can substitute k into the equation to get the general equation that relates p and q:
p*q = 2
or
p = 2/q
Therefore, the equation that relates p and q is p = 2/q, where p and q are variables that vary inversely and 2 is the constant of proportionality.
Step-by-step explanation:
Supplementary angles have a measure of how many degrees
A)90 degrees
B)360 degrees
C)equal
D)180 degrees
Supplementary angles have a measure of 180 degrees
Stacy’s Dress Shop received a $1,110 invoice dated July 14 with 4/10, 3/15, n/60 terms. On July 28, Stacy’s sent a $248 partial payment.
What credit should Stacy’s receive?
What is Stacy’s outstanding balance?
1. The credit which Stacy's will receive is $255.670.97.
2. Stacy's outstanding balance will be $854.33.
What credit should Stacy’s receive?A credit refers to the ability of a customer to obtain goods or services before payment based on trust that payment will be made in the future.
From July 28 - July 14, we have 14 days. We are using the 3% discount.
The Credit receivable =
= Partial payment / (1 - discount rate)
= $248 / (1-0.03)
= $248 / 0.97
= $255.670103
= $255.67
What is Stacy’s outstanding balance?An outstanding balance refers to the amount you owe on any debt that charges interest, like a credit card.
Stacy’s outstanding balance:
= $1,110 - $255.67
= $854.33.
Read more about payment
brainly.com/question/26049409
#SPJ1
Suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19 degree angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest hundredth of an inch if necessary.
PLEASE HELPPP!
The ramp rises 8.79 inches from the lowest point on the ground to the nearest hundredth.
A right angle triangle is what?A right angle triangle has a 90 degree angle as one of its angles. Trigonometric ratios can be used to determine the sides. The length of the fiberboard becomes the hypotenuse of the right triangle that is so constructed. As a result, the ramp rises 8.79 inches from the ground at its tallest point to the closest hundredth.
The opposite side of the right triangle is the height of the ramp that is created.
Hence,
sin 19° = opposite / hypotenuse
sin 19° = h / 27
cross multiply
h = 27 × sin 19°
h = 27 × 0.32556815445
h = 8.79034017034
h = 8.79 inches.
To know more about right angle visit:-
https://brainly.com/question/27403620
#SPJ1
is y= |x| + 4 a relation or function
The answer you're probably wanting is "function," since it is a function.
Technically though, it's both. A function is a relation, one where each x-value (or input) has exactly one y-value (or output). So every function is a relation, but not every relation is a function.
Apple has a sale for new iPhone 12
.They are selling the phones for $795
. That is a 35% mark up from their wholesale priceWhat is Apples' cost for the iPhone 12?
Cost price of iPhone12 is $588.89
To determine Apple's cost for the iPhone 12, we need to work backwards from the retail price of $795 and account for the 35% mark-up.
If we assume that the retail price includes the mark-up and the wholesale price is the original cost price of the product, we can set up an equation to solve for the cost:
Cost + 35% of Cost = Retail Price
Let's simplify the equation by converting the percentage to a decimal:
Cost + 0.35Cost = $795
Combining like terms:
1.35Cost = $795
Dividing both sides by 1.35:
Cost = $588.89
Therefore, Apple's cost for the iPhone 12 is approximately $588.89. This means that Apple makes a profit of $206.11 per phone sold.
It's important to note that this calculation is based on the assumption that the retail price includes only the 35% mark-up and not additional costs such as marketing, shipping, and other expenses that Apple incurs. Additionally, the actual wholesale cost may vary depending on a number of factors such as production volume, component prices, and supplier negotiations.
While we can estimate Apple's cost for the iPhone 12 based on the mark-up and retail price, it's important to keep in mind that the actual cost and profit margins may be more complex and variable in reality.
To know more about Cost Price here:
https://brainly.com/question/19104371
#SPJ1
This is the bone density score separating the bottom, 7% from the top 93%
This means that bone density scores below -1.88 are in the bottom 7% of scores, and scores above 1.88 are in the top 93% of scores.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
It is relates to bone density score distribution, where the bottom 7% of scores are separated from the top 93% of scores. This could be interpreted in a few different ways, but here's one way to approach it:
If we assume that the bone density scores are normally distributed (which is a common assumption in statistics), then we can use the properties of the normal distribution to estimate the cutoff values for the bottom 7% and top 93% of scores.
The standard normal distribution has a mean of 0 and a standard deviation of 1. Using this distribution, we can look up the cutoff values for the bottom 7% and top 93% of scores using a standard normal distribution table or calculator. These cutoff values represent the bone density scores below which 7% of scores fall and above which 93% of scores fall.
For example, using a standard normal distribution table, we can find that the cutoff value for the bottom 7% of scores is approximately -1.88, and the cutoff value for the top 93% of scores is approximately 1.88.
Therefore, This means that bone density scores below -1.88 are in the bottom 7% of scores, and scores above 1.88 are in the top 93% of scores.
To learn more about Algebraic expression from given link.
brainly.com/question/953809
#SPJ1
look at image please
The normal distribution is X ~ N(17, 0.8), the median is equal to mean which is 17 feet, the z-score is 2.5, the probability that a randomly selected giraffe will be shorter than 18 feet tall is 0.8944.
What is the distribution of Xa. The distribution of X is normal, which we can write as X ~ N(17, 0.8).
b. Since the normal distribution is symmetric, the median is equal to the mean, which is 17 feet.
c. To find the z-score for a giraffe that is 19 feet tall, we use the formula:
z = (x - μ) / δ
where x is the height of the giraffe, mu is the mean height of the population (17 feet), and sigma is the standard deviation (0.8 feet). Plugging in the values, we get:
z = (19 - 17) / 0.8 = 2.5
So the z-score for a giraffe that is 19 feet tall is 2.5.
d. To find the probability that a randomly selected giraffe will be shorter than 18 feet tall, we need to find the area under the normal distribution curve to the left of x = 18. We can use a standard normal distribution table or a calculator to find this area, or we can standardize the value of x and use the standard normal distribution table or calculator. Using the latter method, we have:
z = (x - μ) / δ = (18 - 17) / 0.8 = 1.25
Looking up the area to the left of z = 1.25 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.8944. So the probability that a randomly selected giraffe will be shorter than 18 feet tall is 0.8944.
e. To find the probability that a randomly selected giraffe will be between 16.7 feet and 17.5 feet tall, we need to find the area under the normal distribution curve between x = 16.7 and x = 17.5. Again, we can standardize the values of x and use a standard normal distribution table or calculator. We have:
z1 = (16.7 - 17) / 0.8 = -0.38
z2 = (17.5 - 17) / 0.8 = 0.63
Looking up the area between z1 = -0.38 and z2 = 0.63 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.2981. So the probability that a randomly selected giraffe will be between 16.7 feet and 17.5 feet tall is 0.2981.
f. The 90th percentile for the height of the giraffe is the height x such that 90% of the giraffes have a height below x. In other words, we need to find the value of x such that the area under the normal distribution curve to the left of x is 0.9. Using a standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile, which is approximately 1.28. We can then use the formula for z-score to find the corresponding height x:
z = (x - μ) / δ
1.28 = (x - 17) / 0.8
Solving for x, we get:
x = 17 + 1.28 * 0.8 = 18.024
So the 90th percentile for the height of the giraffe is 18.024 feet.
Learn more on normal distribution here;
https://brainly.com/question/4079902
#SPJ1
Two concentric circles have radii of 14 and 16. Find the area of the ring. Round to the nearest tenth.
The area of the ring formed by concentric circles is approximately 188.5 square units.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The ring is formed by two concentric circles.
The area of the ring can be found by subtracting the area of the smaller circle from the area of the larger circle.
The area of a circle with radius r is given by the formula A = πr².
So, the area of the larger circle with radius 16 is -
A1 = π(16)² = 256π
And the area of the smaller circle with radius 14 is -
A2 = π(14)² = 196π
Therefore, the area of the ring is -
A ring = A1 - A2
A ring = 256π - 196π
A ring = 60π
To round to the nearest tenth, we can approximate π as 3.14 -
A ring ≈ 60 × 3.14 = 188.4
Rounding to the nearest tenth, we get -
A ring ≈ 188.4 ≈ 188.5
Therefore, the area of the ring is 188.5 square units.
To learn more about area from the given link
https://brainly.com/question/25292087
#SPJ1
For the figures given in the first column, match their corresponding values of x.
answer options:
6√3
4√2
The corresponding values of x for the given figures are 1. 4√2 and 2. 6√3.
What is sine function?The ratio of a right-angled triangle's hypotenuse to its opposite side is known as the sine function in trigonometry. Use the sine function to get the unknown angle or sides of a right triangle. The sine of an angle in a right-angled triangle is the proportion between the hypotenuse and the side parallel to the angle.
The sine function defines the relationship between the opposing side and the hypotenuse.
For the first figure we can write:
sin (45) = opposite side / hypotenuse = x / 8
1/√2 = x/8
x = 8/√2 = 4√2.
For the second figure we have:
sin 60 = opposite side / hypotenuse
√3/2 = x/12
x = 12√3/2 = 6√3
Hence, the corresponding values of x for the given figures are 1. 4√2 and 2. 6√3.
Learn more about sine function here:
https://brainly.com/question/4406079
#SPJ1
What is y = -4x + 11 , 3x + y =9
The AP Chemistry class is mixing 100 pints of liquid together for an experiment. Liquid A contains 10% acid, liquid B contains 40% acid, and liquid C contains 60% acid. If there are twice as many pints of liquid A than liquid B, and the total mixture contains 45% acid, find the number of pints needed for each liquid.
Therefore, they need 25 pints of liquid A, 12.5 pints of liquid B, and 62.5 pints of liquid C to make the final mixture.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables, and the goal is to solve for the value(s) of the variable(s) that make the equation true.
Given by the question.
Let's denote the number of pints of liquid A, B, and C as A, B, and C, respectively. We know that:
A + B + C = 100 (since they are mixing 100 pints in total)
We also know that the concentration of acid in the final mixture is 45%, so:
0.1A + 0.4B + 0.6C = 0.45(100) = 45
Finally, we are told that there are twice as many pints of liquid A as liquid B, so:
A = 2B
We can use these three equations to solve for A, B, and C. First, substitute A = 2B into the equation A + B + C = 100:
2B + B + C = 100
3B + C = 100
Next, substitute A = 2B into the equation 0.1A + 0.4B + 0.6C = 45:
0.1(2B) + 0.4B + 0.6C = 45
0.2B + 0.4B + 0.6C = 45
0.6B + 0.6C = 45
Simplify this equation by dividing both sides by 0.6:
B + C = 75
We now have two equations with two variables:
3B + C = 100
B + C = 75
Subtracting the second equation from the first, we get:
2B = 25
B = 12.5
Substituting this value back into B + C = 75, we get:
12.5 + C = 75
C = 62.5
Finally, using A = 2B, we get:
A = 25
To learn more about equation:
https://brainly.com/question/29657992
#SPJ9
Martina's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Martina $4.30 per pound, and type B coffee costs $5.55 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $689.00. How many pounds of type A coffee were used?
Hence, in response to the provided question, we can say that Martina equation used 26 pounds of type A coffee in the mix as a result.
What is equation?An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.
Assume Martina used x pounds of type A coffee in her blend. Then, based on the information provided, she used 4 pounds of type B coffee.
Type A coffee costs $4.30 per pound, so x pounds of type A coffee costs $4.30x dollars.
Because the entire cost of the blend is given as $689.00, we may formulate the following equation:
4.30x + 22.20x = 689.00
Mixing similar phrases yields:
26.50x = 689.00
When we divide both sides by 26.50, we get:
x = 26
Martina used 26 pounds of type A coffee in the mix as a result.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Which of the following best describes the equation below?
y=x/3
A. neither a relation nor a function
B. both a relation and a function
C. relation only
D. function only
In a large population, 67% of the households have cable tv. A simple random sample of 64 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions?
Answer:
The mean of the sampling distribution of the sample proportions is the same as the population proportion, which is 0.67.
The standard deviation of the sampling distribution of the sample proportions can be calculated using the formula:
σp = sqrt [p * (1 - p) / n]
where p is the population proportion (0.67), n is the sample size (64), and σp is the standard deviation of the sampling distribution of the sample proportions.
Plugging in the values, we get:
σp = sqrt [0.67 * (1 - 0.67) / 64]
= sqrt [0.2211 / 64]
= 0.061
Therefore, the standard deviation of the sampling distribution of the sample proportions is 0.061.
Can some math experts try to help me with this questions please? No random answer please.
Answer:
1. Pick an object in your house that is parabolic. As an example, I will use a banana.
2. Measure its height and width.
My banana's height is 3 in, and its width is 7 in.
(see the attached image)
3. Show the parabola made by the object on a Cartesian (rectangular) plane.
(see the attached graph)
4. The approximate quadratic for that graph is:
y = (1/4)x²