Answer:
x = 21
Step-by-step explanation:
(x-6) /3 = 5
Multiply each side by 3
(x-6) /3 * 3 = 5*3
x-6 = 15
Add 6 to each side
x-6+6 = 15+6
x = 21
Josie ran a lap in 45.23 seconds.
Erica ran a lap in 43.11 seconds. How
much longer did it take Josie to rut
the lap?
Answer: 2.12 seconds
Step-by-step explanation:
From the question, we are informed that Josie ran a lap in 45.23 seconds while Erica ran a lap in 43.11 seconds.
To calculate the extra amount of time it took Josie to complete the lap, we subtract Erica's time from Josie's time. This will be:
= 45.23 seconds - 43.11 seconds
= 2.12 seconds
Look at the picture
Answer:
Your answer is E
Step-by-step explanation:
To make sure, plug the values in the place of N
[tex]-2 <-1, 0, 1, 2, 3, 4, 5, 6, \\ -1, 0, 1, 2, 3, 4, 5, 6, \leq 6[/tex]
I WILL MARK BRAINLIEST IF ANSWER IN LESS THAN 5 MINUTES!!!!!!! tory is buying bananas. she has 15 dollars and bananas are 2.45 each. how many bananas can she buy?
Answer:
6 bananas
Step-by-step explanation:
Divide the dollars by the price for bananas
15/2.45
6.12244898
Round down because she cannot buy part of a banana
6 bananas
Planes A and B intersect.
Which describes the intersection of line m and line n?
m
O point w
O point X
O point Y
O point Z
Answer:
Hello!
____________________
Your answer would be (A) O point W.
Step-by-step explanation: Intersection of the two lines is defined as the point where the two lines cross or meet each other.
It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.
From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.
Hence, option A is correct.
Hope this helped you!
Answer: point w hope this helped
Step-by-step explanation:
The Egyptians used a ramp
that could hold 1,000 pounds.
If 6 people got on the ramp
and they weighed 780 pounds
total. What percentage of the
ramp's weight capacity is still
available?
Answer:
22%
Step-by-step explanation:
Well if the ramp can hold 1000lbs and 6 people all weight 780 in total (they must be really fat lol, but anyway) we can make the following fraction.
780/1000
So now we simplify the fraction to 39/50.
And do 39 / 50 = .78
To make that a percent we move the decimal point 2 times to the right so 78% of the ramp‘s capacity is being used meaning there is stil 22% capacity left.
The perimeters of two similar figures are 15 in. and 24 in. What is the ratio of the areas of the two figures? State your answer as a fraction.
Answer:
25/64
Step-by-step explanation:
ratio of perimeters = 15/24 = 5/8
ratio of areas = square of ratio of perimeters
ratio of areas = (5/8)^2 = 25/64
(10 power 5) power 3 ...... Need help pls
Answer:
10power 15
Step-by-step explanation:
You keep the base, and you multiply the powers which means
5✖️3=15
base=10
10power 15
Select the points that are solutions to the system of inequalities select all that apply
Answer:
B. (2, 4)
D. (10, -1)
Step-by-step explanation:
The solution sets must be in the shaded region of the systems of inequalities. It cannot be on either lines because both lines are dotted. In that case, only B and D work because they are inside the shaded regions while the other points are not.
Answer:
B. (2, 4)
D. (10, -1)
Step-by-step explanation:
To be a solution, a point must be in the shaded part of the graph.
Answer: (2, 4), (10, -1)
Factor 24m - 12p 72 to identify the equivalent expressions. choose two answers Choices: A.6(4m 2p 12) B.2(12m-6p 36) C.12(2m-p 6) D.24(m-12p 3)
Answer:
thats tough
Step-by-step explanation:
At the beginning of an experiment, a scientist has 356 grams of radioactive goo. After 210 minutes, her sample has decayed to 44.5 grams. Find a formula for G ( t ) , the amount of goo remaining at time t . Keep at least 5 decimal places.
Answer: [tex]\bold{G(t)=356e^{-0.59413t}}[/tex]
Step-by-step explanation:
Use the decay formula: [tex]P=P_oe^{kt}[/tex] where
P is the remaining amount of the sampleP₀ is the original amount of the samplek is the decay ratet is the time (in hours)Given: P = 44.5, P₀ = 356, k = unknown, t = 210 minutes (3.5 hours)
[tex]44.5=356e^{k(3.5)}\\\\\\\dfrac{44.5}{356}=e^{3.5k}\\\\\\0.125=e^{3.5k}\\\\\\ln(0.125)=3.5k\\\\\\\dfrac{ln(0.125)}{3.5}=k\\\\\\-0.59413=k[/tex]
Input P₀ = 356 and k = -0.59413 into the decay formula
[tex]\large\boxed{P=356e^{-0.59413t}}[/tex]
our boss is a biologist who needs wood samples from long-leaf pine trees with a fungal disease which is only visible under a microscope, and she sends you on an assignment to collect the samples. She wants at least 50 different diseased samples. She tells you that approximately 28% of long-leaf pine trees currently have the fungal disease. If you sample 160 long-leaf pine trees at random, what is the probability you’ll have at least 50 diseased samples to return to your boss? (Use the normal approximation to calculate this probability and chose the closest answer to the question.)
Answer:
Step-by-step explanation:
In this scenario, the probability of success, p is 28% = 28/100 = 0.28
Number of samples, n = 160
Probability of failure, q = 1 - p = 1 - 0.28 = 0.72
Mean,µ = np = 0.28 × 160 = 44.8
Standard deviation, σ = √npq = √160 × 0.28 × 0.72 = 5.68
Let x be the random variable representing the number of wood samples from long-leaf pine trees with a fungal disease. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
the probability that you’ll have at least 50 diseased samples to return to your boss is expressed as
P(x ≥ 50) = 1 - P(x < 50)
For P(x < 50)
z = (50 - 44.8)/5.68 = 0.91
Looking at the normal distribution table, the probability corresponding to the z score is 0.819
Therefore,
P(x ≥ 50) = 1 - 0.819 = 0.181
What is the value of x ?
Answer:
25
Step-by-step explanation:
180-(21+73+51)=25
Hey there! :)
Answer:
C. m∠x = 35°.
Step-by-step explanation:
Begin by finding the value of the third angle of the triangle. Recall that all interior angles of a triangle sum up to 180°:
180 - 73 - 51 = 56°.
Since the top angle is split into x and 21°, simply subtract to solve for x:
56 - 21 = 35°. Therefore:
m∠x = 35°.
Simplify the expression -3÷(-3/5)
Answer:
the answer is 5 if it was helpful please give 5 star
Which is a perfect square?
6’1
6’2
6’3
6’5
Answer:
6^2 is the answer
Step-by-step explanation:
just trust me ik
HELPPPP ME ASAP PLEASEEE DO STEP BY STEPPPP Distribute and simplify the following: x(3x + 2)(-2x + 1)
Answer:
-6x^3 - x^2 + 2x
Step-by-step explanation:
We can first start with distributing the x using the distributive property
(3x^2 + 2x)(-2x+1) Remember that when x is multiplied with 3x, it increases the exponent to 3x^2)
Now we use FOIL to distribute (First, Outside, Inside, Last)
-6x^3 + 3x^2 - 4x^2 + 2x
We can combine the like terms (3x^2 and - 4x^2) into -x^2
-6x^3 - x^2 + 2x
The sum of the first two terms of an infinite GP is 6 and each term is 5 times the sum of the succeeding termsthen the second term GP is
Answer:
[tex]\dfrac{6}{7}[/tex].
Step-by-step explanation:
It is given that the sum of first two terms of an infinite GP is 6.
nth term of a GP is
[tex]a_n=ar^{n-1}[/tex]
[tex]a+ar=6[/tex] ...(1)
Each term is 5 times the sum of the succeeding terms.
[tex]a_n=5(a_{n+1}+a_{n+2}+...+\infty)[/tex]
[tex]ar^{n-1}=5(ar^n+ar^{n+1}+...+\infty)[/tex]
[tex]ar^{n-1}=5ar^n(1+r+r^2+...+\infty)[/tex]
Divide both sides by a.
[tex]r^{n-1}=5r^n(\dfrac{1}{1-r})[/tex] [tex][\text{Sum of infinite GP}=\dfrac{a}{1-r}][/tex]
[tex]\dfrac{r^n}{r}=\dfrac{5r^n}{1-r}[/tex]
[tex]\dfrac{1}{r}=\dfrac{5}{1-r}[/tex]
[tex]1-r=5r[/tex]
[tex]1=6r[/tex]
[tex]\dfrac{1}{6}=r[/tex]
The common ratio is 1/6.
Put r=1/6 in (1).
[tex]a+a(\dfrac{1}{6})=6[/tex]
[tex]6a+a=36[/tex]
[tex]7a=36[/tex]
[tex]a=\dfrac{36}{7}[/tex]
Second term [tex]ar=\dfrac{36}{7}\times \dfrac{1}{6}=\dfrac{6}{7}[/tex]
Therefore, the second term is [tex]\dfrac{6}{7}[/tex].
PLEASE HELP Use the squared identities to simplify 2cos2x cos2x.
Answer:
D
Step-by-step explanation:
The correct option is option D as 2cos²(x)cos²(x) simplifies as follows:
2cos²(x)cos²(x) = {3 + 4cos(2x) + cos(4x)} / 4
Simplification:The given expression is : 2cos²(x)cos²(x)
The square identity for cosine is given by:
2cos²(x) -1 = cos(2x)
Thus,
2cos²(x) = {cos(2x) +1}
simplifying again,
cos²(x) = {cos(2x) +1}/2
Simplifying the above using squared identities:
2cos²(x)cos²(x) = {cos(2x) +1}cos²x
= {cos(2x) +1} {{cos(2x) +1}/2}
[tex]= \frac{\{cos(2x) +1\}^2}{2}\\\\=\frac{cos^2(2x)+2cos(2x)+1}{2}\\\\=\frac{\frac{cos(4x)+1}{2}+2cos(2x)+1}{2}\\\\=\frac{3+4cos(2x)+cos(4x)}{4}[/tex]
so,
2cos²(x)cos²(x) = {3 + 4cos(2x) + cos(4x)} / 4
Hence option D is correct.
Learn more about squared identities:
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The builder receives a 20% contractor's discount, plus and additional 3% for paying in full within 30 days. Tax on building materials is 5%. What is the total bill including discounts and taxes?
Answer:
$1340.49
Step-by-step explanation:
From the attached image
Subtotal Cost of Purchased Items
[tex]= (20 \times 16.69)+(2 \times 20.78)+(2 \times 15.58)+(6 \times 21.38)\\+(118 \times 6.60)+(500 \times 0.22)+(10 \times 8.44)+(1 \times 150)\\\\=\$1658[/tex]
Since the builder receives a 20% contractor's discount, plus and additional 3% for paying in full within 30 days.
Discount = 23% of $1658 = 0.23 X 1658 =$381.34
Total (Less Discount) = 1658-381.34 = $1276.66
Tax on building materials is 5%.
Therefore:
Tax = 5% of $1276.66=0.05 X 1276.66
Tax=$63.83
Therefore, the total bill:
=$1276.66+63.83
Grand Total =$1340.49
A baseball team plays in a stadium that holds 50000 spectators. When the ticket price is $10, the average attendance is 27000. When the price is lowered to $6, the average attendance rose to 39000. Find a demand function, D(q), where q is the quantity or number of spectators and D(q) is linear.
Answer:
the answer is below
Step-by-step explanation:
Demand seems to be based on price.
Therefore we must consider two things:
that "x" is equal to the price and that "y" is equal to the average attendance.
Thus:
the two points would be:
(x1, y1) = (10,27000)
(x2, y2) = (6.39000)
The slope of a straight line is given by:
m = (y2-y1) / (x2-x1)
we replace:
m = (39000 - 27000) / (6 - 10) = 12000 / -4 = -3000
The equation of a straight line can be expressed like this
y = m * x + b.
where
m is the slope and b is the y-intercept.
we replace
y = -3000 * x + b.
To solve for b, replace x and y with the value of one of the points on the line.
We choose (6.39000). and we replace:
39000 = -3000 * 6 + b
39000 = -18000 + b
39000 + 18000 = b
b = 57000.
if we replace we have:
the equation becomes y = -3000 * x + 57000
since it is the demand and * x is the price.
t = d (x), therefore the equation becomes
d (x) = -3000 * x + 57000.
d (x) = 57000 - 3000 * x.
when x = 0, the price is 0 and the demand will be 57000, which will be more than the stadium can contain because the stadium can only contain 50,000.
So:
when x = 6, the price is 6 and the demand is 57000 - 18000 = 39000.
when x = 10, the price is 10 and the demand is 57000 - 30000 = 27000.
Write an equation for the following: a) The ellipse has foci (2, 0) and (–2, 0) and vertices (4, 0) and (–4, 0). b) The ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal.
Answer:
a) [tex]\frac{x^2}{16} +\frac{ y^2}{12} = 1[/tex]
b) [tex]\frac{x^2}{64} +\frac{ y^2}{16} = 1[/tex]
Step-by-step explanation:
a)
The vertices are located in the x-axis, so we have a horizontal ellipse.
The equation of an ellipse is given by:
[tex]\frac{(x - h)^2}{a^2} +\frac{ (y - k)^2}{b^2} = 1[/tex]
The coordinates of the foci and the vertices are given by:
Foci: [tex]F(h \pm c, k)[/tex]
Vertices: [tex]V(h\pm a, k)[/tex]
Comparing the coordinates with the values given, we have that:
h = 0, k = 0, c = 2, a = 4
To find the value of b we can use the following equation:
[tex]c^2 = a^2 - b^2[/tex]
[tex]4 = 16 - b^2[/tex]
[tex]b^2 =12[/tex]
So the equation of the ellipse is:
[tex]\frac{x^2}{16} +\frac{ y^2}{12} = 1[/tex]
b)
If the ellipse is centered at the origin, we have:
h = 0, k = 0
The major axis is 'a' and the other axis is 'b', so we have:
a = 8, b = 4.
So the equation is:
[tex]\frac{x^2}{64} +\frac{ y^2}{16} = 1[/tex]
How do I solve this?
Answer:
See below.
Step-by-step explanation:
[tex](5x^2y^3)^0\div(-2x^{-3}y^5)^{-2}[/tex]
First, note that everything to the zeroth power is 1. Thus:
[tex]=1\div(-2x^{-3}y^5)^{-2}=\frac{1}{(-2x^{-3}y^5)^{-2}}[/tex]
Distribute using Power of a Power property:
[tex]=\frac{1}{(-2)^{-2}(x^{-3})^{-2}(y^5)^{-2})}[/tex]
Make the exponents positive by putting them to the numerator:
[tex]=\frac{(-2)^2(x^{-3})^2(y^5)^2}{1}[/tex]
[tex]=\frac{4x^{-6}y^{10}}{1}[/tex]
Make the exponent positive by this time putting it to the denominator:
[tex]=\frac{4y^{10}}{x^6}[/tex]
3kg of butter is packed into small packets of 75gm each to be supplied to a restaurant. How many such packets can be made? If 10 such small packets are put into a box, how many such boxes can be made?
Answer:
4
Step-by-step explanation:
Converting 3kg to grams,
3 kg * = 3000 g
If we divide 3000 g by 75, we will determine how many packets of butter there are.
3000 / 75 = 40.
40 packets of butter. If 10 go into a box, that means that
40 / 10 = 4 boxes.
Hence 4 such boxes can be made
Answer:
4 boxes can be made
Step-by-step explanation:
→ First work out the amount of small packets there are
3 kg = 3000g
3000 ÷ 75 = 40
→ Now we know that there are 40 small packets and one box can hold 10 packets so,
1 box = 10 packets
? boxes = 40 packets
40 ÷ 10 = 4
→ 4 boxes can be made
which is the smallest number 6.1 5.4 5 1/10 6 7/10
Answer:
5 1/10
Step-by-step explanation:
Convert all integers to decimals.
6.1
5.4
5 1/10 = 5.1
6 7/10 = 6.7
The smallest number frrom the list is 5.1 or 5 1/10.
Answer:
5 1/10
Step-by-step explanation:
Convert to the same format, IE. decimals so you can compare like numbers. The other numbers are:
6.1
5.4
5.1 (1/10 = 0.1)
6.7 (7/10 = 0.7)
So, from least to greatest they are:
5.1
5.4
6.1
6.7
❗️5 points❗️
2. Find the slope of the line.
A. 3
B. -3
C. -1/3
D. 1/3
Answer:
D. 1/3
Step-by-step explanation:
Use the following equation to solve for the slope:
m (slope) = (y₂ - y₁)/(x₂ - x₁).
Let:
(x₁ , y₁) = (0 , 2)
(x₂ , y₂) = (3 , 3)
Plug in the corresponding numbers to the corresponding variables:
m = (3 - 2)/(3 - 0)
m = (1)/(3)
m = 1/3
D. 1/3 is your answer.
~
Which statement is true about the ranges for the box plots? A variety of two types of snack packs are delivered to a store. The box plots compare the number of calories in each snack pack of crackers to the number of calories in each snack pack of trail mix.
*The box plots are shown in the attachment
Answer/Step-by-step explanation:
Range is the difference between the largest value of a data set and the lowest value in that data set.
In a box plot, the highest value is located at the end of the whisker to our right, while the lowest value is located at the beginning of the whisker of the box plot at our left.
For Crackers, the range = 100-70 = 30
For Cookies, the range = 115-70 = 45
Therefore, we can conclude that the range value of the number of calories in crackers (30) is less/lower than that of cookies (45).
Answer: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
What is the solution to the system of equations? 6 x + 2 y = 6. 7 x + 3 y = 5. (Negative 3, 2) (Negative 1, 6) (2, Negative 3) (6, Negative 1)
Answer:
(2, -3)
Step-by-step explanation:
These are the steps I used:
(6x+2y=6) x3 -> 18x+6y=18
(7x+3y=5) x2 -> 14x+6y=10
When you subtract the equations you get:
4x=8
x=2
The solution to the system of equations is -3 and -2
The correct option is A
What is a system of equations?A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one.
6x+2y=6 is equation (1)
7x+3y=5 is equation (2)
Multiplying equation (1) by (3)
18x+6y=18 is equation(3)
By multiplying (2) by 2
14x+6y=10 is equation (4)
Substrate equation (4) from (3)
4x=8 Now, divide both sides by 4
X=2
Substitute x=2 in (1)
6(2)+2y=6
12+2y=6
Substrate 12 from LHS and RHS
2y=-6
Divide both sides by 2
y=-3
Hence x=2 and y=-3
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express -64/112as a rational number with denominator 7. plz explain
Answer:
Step-by-step explanation:
=-3.875/7. (divided by 16)
Find the number of 4-digit numbers that contain at least three even digits.
Answer:
1234
Step-by-step explanation:
Answer:
2625
Step-by-step explanation:
First let's see all the possible combinations.
(Even=E, Odd= O)
1) EEEO
2) EEOE
3) EOEE
4) OEEE
5) EEEE
Now let's see what E and O possibly could be
E = 0, 2, 4, 5, 6 and 8 (5)
O = 1, 3, 5, 7, 9 (5)
Now we are just simply gonna multiply
1) EEEO = 4*5*5*5
2) EEOE = 4*5*5*5
3) EOEE = 4*5*5*5
4) OEEE = 5*5*5*5
5) EEEE = 4*5*5*5
The even contains a 0, so you can't put 0 in, so (5-1=4), there are only 4 digits for the even.
500 times 4 = 2000
5⁴ = 625
2000+625= 2625
Find the area in square centimeters of the composite shape shown below. Enter only a number as your answer.
Answer:
136 cm^2
Step-by-step explanation:
you can divide the shape into two shapes:
first : draw a line ⊥ to BC from point E to point F
rectangle : DCEF : Area = L*W=7*13=91 cm^2
the other shape AEBF is a trapezoid:
Area of AEBF= [(a+b)/2] h where a and b are the base and h is the height
height =18-13=5
a=7, b=11
A=[(7+11)/2]*5=45 cm^2
add the two areas : 45+91=136 cm^2
hope it works, many ways to find the area
Answer:
the answer is 49
Step-by-step explanation:
18+13+11+7=49
Drag each step and justification to the correct location on the table. Each step and justification can be used more than once, but not all steps and justifications will be used.
Order each step and justification that is needed to solve the equation below.
please help me
Answer/Step-by-step explanation:
Below are the steps to take in solving the given equation, as well as justification forf each step:
[tex] \frac{2}{3}y + 15 = 9 [/tex] => Given
[tex] \frac{2}{3}y + 15 - 15 = 9 - 15 [/tex] => subtraction property of equality
[tex] \frac{2}{3}y = - 6 [/tex] => simplification
[tex] \frac{2}{3}y * \frac{3}{2} = - 6 * \frac{3}{2} [/tex] => multiplication property of equality
[tex] y = - 9 [/tex] => simplification