Answer:
(2x + 1) (x - 4)
Step-by-step explanation:
2x² - 7x - 4.
need two number that add up to -7, but that multiply together to get -4.
(2x + 1) (x - 4) = 2x² - 4(2x) + x - 4 = 2x² - 8x + x - 4 = 2x² - 7x - 4
The ages of members of a stamp collecting group are normally distributed with a mean of 55 years and a standard deviation of 4 years.
There are 104 members in the group.
About how many members are expected to be between 51 years old and 59 years old?
About 71 members of the group are expected to be between 51 years old and 59 years old.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.Considering the mean of 55 years and the standard deviation of 4 years, ages between 51 and 59 years are within one standard deviation of the mean, hence the percentage is of:
68%.
Out of 104 people, the number of people with ages in the range is given as follows:
0.68 x 104 = 71 people. (rounded to the nearest integer).
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In a group of 80 people, 50 like tea, 30 like coffee and 20 like tea only.
a) find the number if people who like both drink
b)find the number of people who like either of the drinks
Answer:
60 and 40
Step-by-step explanation:
a) To find the number of people who like both tea and coffee, we can use the formula:
Number of people who like both = Number of people who like tea + Number of people who like coffee - Number of people who like only teaPlugging in the given values, we get:
Number of people who like both = 50 + 30 - 20 = 60Therefore, there are 60 people who like both tea and coffee.
b) To find the number of people who like either of the drinks, we can add the number of people who like tea only, the number of people who like coffee only, and the number of people who like both tea and coffee. Mathematically,
Number of people who like either drink = Number of people who like tea only + Number of people who like coffee only + Number of people who like both tea and coffeePlugging in the given values, we get:
Number of people who like either drink = 20 + (30-60) + 50 = 40Therefore, there are 40 people who like either tea or coffee (or both).
PLEASE HELP I WILL MARK YOU BRAINLIEST!!
Answer:
96π
Step-by-step explanation:
the shape is made up of a cylinder and a cone.
Volume of cylinder = π r ² h
= π (3)² (9)
= 81π.
Volume of cone = (1/3) X vertical height X π r ²
= (1/3) (5) π (3)²
= 15π
volume of composite solid = 81π + 15π = 96π
PLEASE HELP ASAP Brainiest 100 points
Scale Factor
An engineer has a 60:1 scale drawing of a bridge. The dimensions of the scaled bridge deck are 36 inches by 4 4/5. What is the area of the actual bridge deck in square feet? 6,912 square feet
4,320 square feet
576 square feet
72 square feet
The actual bridge deck measures 4,320 square feet in size.
First, we need to convert the scaled dimensions to actual dimensions. Since the scale is 60:1, we need to multiply the scaled dimensions by 60 to get the actual dimensions.
The scaled length of the bridge deck is 36 inches, so the actual length is:
36 inches x 60 = 2,160 inches
The scaled width of the bridge deck is 4 4/5, or 24/5, inches. So the actual width is:
24/5 inches x 60 = 288 inches
To find the area of the actual bridge deck in square feet, we need to convert the actual dimensions to feet and then multiply:
Actual length in feet = 2,160 inches ÷ 12 inches/foot = 180 feet
Actual width in feet = 288 inches ÷ 12 inches/foot = 24 feet
Area in square feet = Actual length x Actual width = 180 ft x 24 ft = 4,320 square feet
Therefore, the area of the actual bridge deck in square feet is 4,320 square feet.
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5. Jada is comparing 2 functions.
a(x) = 2(2)*
b(x) = 4x² + 2x
She finds that a(2) = 8 and a(3) = 16, b(2) = 20 and b(3) = 42. She draws the conclusion
that the larger the x value, a will continue to greater than b as she saw in her 2
examples. Show or explain why Jada is not correct.
After considering the given data we conclude that Jada's conclusion is not correct because she only tested two values of x for each function and concluded that a will always be greater than b for larger x values.
So , this is not true in general. In order to see why, let's provide a specified comparison between the two functions for a general value of x by forming an algebraic expression
a(x) = 2(2) = 4
b(x) = 4x² + 2x
We clearly see that b(x) grows much faster than a(x) as x gets larger. In fact, for any value of x greater than 1/2, b(x) will be greater than a(x).
Then, Jada's conclusion is not correct in general.
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im abt to km$ this is literslly due in a couple of minutes lol
Answer:
x-intercept = -7
y-intercept = 1
rate of change = 1.25
Step-by-step explanation:
X and Y intercept are pretty to find.
Rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
So for our case it will be [tex]\frac{-0.75-(-2)}{-8-(-9)}[/tex]
The answer will be 1.25
Please help! What is the surface area of the cylinder with a height 4 m and radius 8 m? Round your answer to the nearest thousandth.
If u answer correctly u get 5 dollars on cahapp
The surface area of the cylinder is 603.19 square meters
Finding the surface area of the cylinderFrom the question, we have the following parameters that can be used in our computation:
Radius, r = 8 meters
Height, h = 4 meters
Using the above as a guide, we have the following:
Surface area = 2πr(r + h)
Substitute the known values in the above equation, so, we have the following representation
Surface area = 2π * 8 * (8 + 4)
Evaluate
Surface area = 603.19
Hence, the surface area is 603.19 square meters
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Solve for x. Assume that lines which appear tangent are tangent.
The value of x using Tangent - Secant theorem is: 16
How to solve the Tangent-secant Theorem?The tangent-secant theorem states that when a tangent and secant possess a common endpoint outside the circle the product of the secant and the external part of the secant is equal to the square of the tangent.
We are given:
internal part of the secant = (x + 9),
external part of the secant = 9,
tangent = 15,
According to Tangent-secant Theorem:
(x + 9) * 9 = 15²
9x + 81 = 225
9x = 144
x = 144/9
x = 16
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 48 minutes of calls is $17.01 and the monthly cost for 86 minutes is $21.95. What is the monthly cost for 56 minutes of calls?
The monthly cost for 56 minutes of calls is given as follows:
$18.05.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.For 38 minutes of call, the price increases by $4.94, hence the slope of the linear function, representing the cost per minute, is given as follows:
m = 4.94/38
m = 0.13.
56 minutes is 30 minutes less than 86 minutes, hence the cost is given as follows:
C(56) = 21.95 - 30 x 0.13
C(56) = $18.05.
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Question 22 of 25
Given below are lease terms at the local dealership. What is the total cash
due at signing?
Terms:
Length of lease: 30 months
. MSRP of the car: $15,500
.
• Purchase value of the car after lease: $9900
• Down payment: $2500
Monthly payment: $425
• Security deposit: $375
Acquisition fee: $500
●
●
OA. $3800
B. $375
C. $3375
D. $3400
The total cash due at signing is $3800.
Option A is the correct answer.
We have,
The total cash due at signing is the sum of the down payment, security deposit, acquisition fee, and the first month's lease payment.
So,
Down payment = $2500
Security deposit = $375
Acquisition fee = $500
First month's lease payment = $425
The total cash due at signing is:
= $2500 + $375 + $500 + $425
= $3800
Thus,
The total cash due at signing is $3800.
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10 ft
15 ft
5 ft
10 ft
5 ft
22 ft
What is the total area that you need to cover?
The total area that needs to be covered which is indicated by the shaded area would be =220ft²
How to calculate the total area that needs to be covered?To calculate the area that needs to be covered, the formula that should be used is the formula for the area of a rectangle which is given below as follows;
Area of rectangule =2( length×width)
where ;
length = 22ft
width = 5ft
area = 2× 22×5
= 220ft²
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At the hot dog stand, it costs $18.39 for five hot dogs and six bags of chips. If it costs $4.63 for one hot dog and two bags of chips, how much is a hot dog?
A hot dog costs 2.25 we get it by solving the equation
Let's denote the cost of one hot dog by x.
Then we can set up two equations:
5x + 6y = 18.39
x + 2y = 4.63
where y is the cost of one bag of chips.
We want to solve for x.
Let us isolate variable y in the second equation
y = 4.63 - x/2
Substitute the y equation in the equation (1)
[tex]$5x + 6\left(\frac{4.63 - x}{2}\right) = 18.39$[/tex]
Simplifying this equation gives:
5x + 13.89 - 3x = 18.39
2x = 4.5
x = 2.25
Hence, a hot dog costs 2.25.
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rewrite the mixed numbers as the sum of whole number and a fraction rewrite the whole number as a sum of fraction each equal to 1
The mixed fraction expression 2³/₄ can be rewritten as: ⁴/₄ + ⁴/₄ + ³/₄
How to write mixed fractions?There are different fractions such as mixed fraction, improper fraction, proper fraction e.t.c.
Now, we are given the fraction as an improper fraction in the form of 2³₄.
Rewriting as a whole number and a fraction gives:
2 + ³/₄
Breaking down the whole number into a fraction is done as:
1 + 1 + ³/₄
= ⁴/₄ + ⁴/₄ + ³/₄
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The average price of a college math textbook is $151 and the standard deviation is $24. Suppose that 40 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.
What is the distribution of
X? X ~ N( , )
For the group of 40, find the probability that the average price is between $152 and $155.
Find the third quartile for the average textbook price for this sample size. $
(round to the nearest cent)
For part b), is the assumption that the distribution is normal necessary? YesNo
(a) The distribution of X is X ~ N(151, 24)
(b) The probability that the average price is between $152 and $155 is 0.950
(c) The quartile for the average textbook price for this sample size is $167.2
(d) The assumption of normal distribution is necessary
(a) What is the distribution of X?Given that
Mean = 151
Standard deviation = 24
The distribution of X is represented as
X ~ N(Mean , Standard deviation)
So, we have
X ~ N(151, 24)
(b) The probability that the average price is between $152 and $155.The z-score is calculated as
z = (x - Mean)/Standard deviation
So, we have
z = (152 - 151)/24 and z = (155 - 151)/24
Evaluate
z = 0.042 and z = 0.167
So, we have
P = P(0.042 < z < 0.167)
Evaluate
P = 0.95044
Approximate
P = 0.950
(c) Finding the third quartileThis is calculated as
Q₃ = Mean + 0.675 * Standard deviation
So, we have
Q₃ = 151 + 0.675 * 24
Evaluate
Q₃ = 167.2
Hence, the quartile for the average textbook price for this sample size is $167.2
(d) Is the assumption necessaryYes, the assumption is necessary
This is because
The distribution has a sample size greater than 25 as required by the central limit theorem
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For positive acute angles � A and � , B, it is known that sin � = 45 53 sinA= 53/45 and cos � = 20 29 . cosB= 29 20 . Find the value of sin ( � − � ) sin(A−B) in simplest form.
The value of sin(θ - φ) = sin(A - B) in simplest form is sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800
How to determine simplest form?Use the trigonometric identity sin(α - β) = sin α cos β - cos α sin β to find sin(θ - φ), where θ = A and φ = B.
First, find cos A and sin B using the given information:
Since sin A = 53/45, use the Pythagorean identity cos² A + sin² A = 1 to find cos A:
cos² A + (53/45)² = 1
cos² A = 1 - (53/45)²
cos A = ± √(1 - (53/45)²)
Since A is a positive acute angle, take the positive square root:
cos A = √(1 - (53/45)²)
Similarly, since cos B = 29/20, use the Pythagorean identity cos² B + sin² B = 1 to find sin B:
sin² B = 1 - cos² B
sin B = ± √(1 - cos² B)
Since B is a positive acute angle, take the positive square root:
sin B = √(1 - (29/20)²)
Use the identity sin(α - β) = sin α cos β - cos α sin β to find sin(A - B):
sin(A - B) = sin A cos B - cos A sin B
= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)
Simplifying this expression:
sin(A - B) = (53/60) - √(2561)/900
Finally, use the identity sin(θ - φ) = sin θ cos φ - cos θ sin φ to find sin(θ - φ) = sin(A - B):
sin(A - B) = sin θ cos φ - cos θ sin φ
= sin A cos B - cos A sin B
= (53/45)(29/20) - √(1 - (53/45)²) √(1 - (29/20)²)
= (53/60) - √(2561)/900
Therefore, the value of sin(θ - φ) = sin(A - B) in simplest form is:
sin(θ - φ) = sin(A - B) = (53 - √(2561))/1800
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I WILL GIVE BRAINLYEST
Answer:
The area is 44
Step-by-step explanation:
If you add the numbers that across from each other you would get 12+12+2+2+8+8= 44
Sort the angles as acute, right, obtuse, or straight.
The top angle is right (90 degrees, kinda looks like a bent elbow).
The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).
The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).
4th is acute.
5th is straight because it's a straight line.
6th is also obtuse.
Have a good day :)
Evaluate 7c1 and 6p4
Answer:
7c1 is an algebraic expression that evaluates to 47. The expression is made up of two terms, 7 and c1. The letter c is a variable and the number 1 represents the exponent of the variable. Therefore, 7 multiplied by the c to the power of 1 is equal to 7 times c, which is equal to 47.
6p4 is an algebraic expression that evaluates to 6,040. The expression is made up of two terms, 6 and p4. The letter p is a variable and the number 4 represents the exponent of the variable. Therefore, 6 multiplied by the p to the power of 4 is equal to 6 times p to the fourth power, which is equal to 6,040.
Calculator What is the area of a sector with a central angle of 144° and a radius of 11 cm? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box. cm² K
Rounding to the nearest hundredth, the area is approximately 151.976 cm².
The formula for the area of a sector is:
A = (θ/360) x πr²
where θ is the central angle in degrees, r is the radius, and π is pi (3.14).
Plugging in the given values, we get:
A = (144/360) x 3.14 x 11^2
A = 0.4 x 3.14 x 121
A = 151.976
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Distance traveled: 84,240,000,000,000 miles away. That is really far!!! /2.5
● Write the distance that Zeek traveled in scientific notation with units.
● Draw a picture of the spacecraft.
Number of
pennies put in
Number of
gumballs
that came out
1 2
1 1
1 3
2 4
1 1
3 1
with work attached
thanks
The required, distance that Zeek traveled in scientific notation with units is 3.3696 × 10¹³ miles.
The distance traveled by Zeek is:
84,240,000,000,000 miles away / 2.5 = 33,696,000,000,000 miles away
We can write this in scientific notation as:
3.3696 × 10¹³ miles
Thus, the required, distance that Zeek traveled in scientific notation with units is 3.3696 × 10¹³ miles.
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Thorium 234 is a radioactive isotope that decays according to the eqaution At=A0e^-10.498t, where A0 is the initial amount present and At is the amount present after t years. is the amount present after t years. If you begin with 1000 grams of strontium 90,
(a) How much thorium 234 will be left after 0.5 years? Round your answer to the nearest tenth of a gram.
------------------- grams
(b) When will 115 grams of thorium 234 be left? Round your answer to the nearest tenth of a year.
-------------------- years
if you need to see the picture here is too. Thank u.
3.6 years will have passed when 115 grams of thorium 234 is left.
(a) To find the amount of thorium 234 left after 0.5 years, we can substitute t = 0.5 and A0 = 1000 into the given equation and solve for At:
[tex]A_t = A0e^{(-10.498t)}\\\\A_t = 1000e^{(-10.498(0.5))}\\\\A_t = 679.6\ grams[/tex]
Therefore, approximately 679.6 grams of thorium 234 will be left after 0.5 years.
(b) To find when 115 grams of thorium 234 will be left, we can set At = 115 in the given equation and solve for t:
[tex]A_t = A_0e^{-10.498t}\\\\115 = 1000e^{-10.498t}\\\\ln(115/1000) = -10.498t\\\\t = 3.6\ years[/tex]
Therefore, approximately 3.6 years will have passed when 115 grams of thorium 234 is left.
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find the derivative of f(x)=(3x^2−4x+1)^4
The derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)
The given function is f(x)=(3x²−4x+1)⁴
We have to find the derivative of the function
By using chain rule we find the derivative
f'(x)=4(3x²−4x+1)³ d/dx(3x²−4x+1)
=4(3x²−4x+1)³ (6x-4)
Hence, the derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)
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The table below models a particular physical situation.
X: -8, 1, 4, 10
Y: 2, -3, 1, -3
Find the piecewise linear equation that models the data above. Round to three decimal places if needed.
_____x + ____ -8 ≤ x ≤ 1
Y= _____x + ____ 1 < x ≤ 4
_____x + ____ 4 < x ≤ 10
The piecewise linear equation is y = -0.556x - 2.444, -8 ≤ x ≤ 1, y = 1.333x - 4.333, 1 < x ≤ 4 and y = -0.667x - 3.667 4 < x ≤ 10
Finding the piecewise linear equationFrom the question, we have the following parameters that can be used in our computation:
X: -8, 1, 4, 10
Y: 2, -3, 1, -3
In the interval [-8, 1], we have
X: -8, 1
Y: 2, -3
A linear equation is represented as
y = mx + c
Using the points, we have
-8m + c = 2
m + c = -3
So, we have
m = -0.556
c = -2.444
So, we have
-0.556x - 2.444, -8 ≤ x ≤ 1
In the interval (1, 4], we have
X: 1, 4
Y: -3, 1
Using the points, we have
m + c = -3
4m + c = 1
So, we have
m = 1.333
c = -4.333
So, we have
1.333x - 4.333, 1 < x ≤ 4
In the interval (4, 10], we have
X: 4 10
Y: 1 -3
Using the points, we have
4m + c = 1
10m + c = -3
So, we have
m = -0.667
c = 3.667
So, we have
-0.667x - 3.667 4 < x ≤ 10
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How do I show a example of using tomato sauce in spaghetti as a ratio? I’m not sure how I can make a math problem and show how to do it. Any advices?
Suppose the credit card company changes the program so Keenan earns 1 mile for every $8 he spends. How would that change the amount of money Keenan needs to spend to earn the miles for his trip?
Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.
If Keenan earns 1 mile for every $8 he spends, then he would need to spend 8 times as much money to earn the same number of miles as he did before.
In other words, he would need to spend $8 to earn 1 mile instead of $1 to earn 1 mile under the old program.
To calculate the new amount of money Keenan needs to spend to earn the miles for his trip, we would need to multiply the old amount by 8.
For example, if under the old program, Keenan needed to spend $10,000 to earn 25,000 miles for his trip, under the new program he would need to spend:
$10,000 x 8 = $80,000
So under the new program, Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.
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If h(x) is a function created by combining two functions by multiplication and h(x) = 2x² + 5x-3, which could be true
of the two component functions?
The component functions must both be linear.
O The component functions must both be quadratic.
The component functions must have y-intercepts with different signs.
The component functions must have increasing or accelerating rates of change.
Answer:
[tex]h(x) = 2 {x}^{2} + 5x - 3[/tex]
[tex]h(x) = (2x - 1)(x + 3)[/tex]
-The component functions must both be linear.
-The component functions must have y-intercepts with different signs.
m/3 = 82°. Find m/4.
m/4= ?
Answer: 98 deg
Step-by-step explanation:
angles 3 and 4 are supplementary; this means their sum is 180 degrees.
so simply put, 180 - angle 3 = angle 4
180 - 82 = 98
Which segments are congruent?
JN and LN
JN and NM
LN and NK
NK and NM
Answer:
LN and NK
Step-by-step explanation:
A perpendicular bisector of a line segment divides the line segment into 2 equal halves.
Here, line JM is a perpendicular bisector of line segment LK at point N. So, line JM divides the line segment LK into 2 equal halves.
The two equal halves are segment LN and segment NK.
Therefore, segment LN is congruent to segment NK.
You purchase a couch for $509.84 plus 4% sales tax. The furniture store offers an installment loan that allows you to pay for the couch by making 12 equal monthly payments of $49.60. What is the cost of credit, in dollars, for this loan? Round your answer to the nearest cent.
What time of day is represented by the figure below? Recall that the rotation of the Earth is counterclockwise.
A. just before sunrise
B. just after sunrise
C. just before sunset
D. just after sunset
Answer:
D
Step-by-step explanation: