Answer:a=17
Step-by-step explanation:
3(4a-8)=180
4a-8=60
4(a-2)=60
a-2=15
a=17
Hope this help!!!!
Find the volume of the solid formed By revolving the region bounded By the graphs of y=x^3, y=1, and x=2 about the line x-axis
Answer:
the y axis will be 1 and the x axis will be 8
I know that the y axis will be 1 because y=1 and I know that the x axis will be 8 because 2 to cubed will be 8 because when you multiply 2 by 2 you get 4 and when you multiply 4 by 2 the answer will be 8 so the axis will be (1,8)
Step-by-step explanation:
Time (hours) 2 4 6 8
Distance (miles) 8 16 24 32
Is the linear relationship also proportional? Explain.
Yes, the constant of proportionality is 4.
Yes, there is no constant of proportionality.
No, the constant of proportionality is 4.
No, there is no constant of proportionality.
The linear relationship between time and distance can be considered proportional. The constant of proportionality in this case is 4.
In a proportional relationship, the ratio between the two quantities remains constant. Here, as time increases by 2 hours, the distance also increases by 8 miles. Let's calculate the ratio of distance to time for each pair of values:
For the first pair (2 hours, 8 miles):
Ratio = distance / time = 8 miles / 2 hours = 4 miles/hour
For the second pair (4 hours, 16 miles):
Ratio = distance / time = 16 miles / 4 hours = 4 miles/hour
For the third pair (6 hours, 24 miles):
Ratio = distance / time = 24 miles / 6 hours = 4 miles/hour
For the fourth pair (8 hours, 32 miles):
Ratio = distance / time = 32 miles / 8 hours = 4 miles/hour
As we can see, the ratio of distance to time remains constant at 4 miles per hour for all the pairs. This indicates a proportional relationship between time and distance.
Therefore, the linear relationship is also proportional, and the constant of proportionality is 4.
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Which of the following is equivalent to
z²+7z-3/z+2
The equivalent expression is:
(z - 1)(z + 3)/(z + 2)
To simplify the expression (z² + 7z - 3)/(z + 2), you can either factorize the numerator or use polynomial division. Let's use factoring in this case.
First, let's factorize the numerator, z² + 7z - 3, into two binomial factors:
(z - 1)(z + 3)
Now, the expression becomes:
[(z - 1)(z + 3)]/(z + 2)
So, the equivalent expression is:
(z - 1)(z + 3)/(z + 2)
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Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and
z ≥ 3.
The total number of integral solutions of x + y + z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and z ≥ 3 is; 59 integer solutions
How to find the number of Integral Solutions?We are given the condition that;
−3 ≤ x ≤ 4
Thus, we will use x values of -3, -2, -1, 0, 1, 2, 3, 4
When;
x = -3 and y = 2, in x + y + z = 12, solving for z gives z = 13
x = -3 and y = 3, in x + y + z = 12, solving for z gives z = 12
x = -3 and y = 4, in x + y + z = 12, solving for z gives z =11
x = -3 and y = 5, in x + y + z = 12, solving for z gives z = 10
x = -3 and y = 6, in x + y + z = 12, solving for z gives z = 9
x = -3 and y = 7, in x + y + z = 12, solving for z gives z = 8
x = -3 and y = 8, in x + y + z = 12, solving for z gives z = 7
x = -3 and y = 9, in x + y + z = 12, solving for z gives z = 6
x = -3 and y = 10, in x + y + z = 12, solving for z gives z = 5
x = -3 and y = 11, in x + y + z = 12, solving for z gives z = 4
Thus, there are 10 solutions with x =-3
Repeating the above with x = -2, we will have 10 solutions
Similarly, with x = -1, we will have 9 more solutions
Similarly, with x = 0, we will have 8 more solutions.
Similarly, with x = 1, we will have 7 more solutions.
Similarly with x = 2, we will have 6 more solutions.
Similarly with x = 3, we will have 5 more solutions.
Similarly with x = 4, we will have 4 more solutions.
Thus,
Total number of solutions = 4 + 5 + 6 + 7 + 8 + 9 + 10 + 10
= 59 integer solutions
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trevor is making a poster for his science project he decides to use 1/2 of the poster for his pictures 3/8 for his hypothesis and 1/4 for the experiment process is this possible explain why or why not
No, it's not possible for Trevor to use 1/2 of the poster for his pictures, 3/8 for his hypothesis, and 1/4 for the experiment process.
How to show it is not possibleThis is discovered by addition of fraction
= 1/2 + 3/8 + 7/8
= 7/8
The fractions 1/2, 3/8, and 1/4 add up to 7/8, which is greater than 1.
Since the fractions represent parts of a whole poster, the total must be less than or equal to 1.
Therefore, Trevor needs to adjust the fractions so that their sum is less than or equal to 1.
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Which of the following ratios is equivalent to 2:3
A) 1/2
B) 4/6
C) 12/13
D)20/25
Answer:
B:4/6
Step-by-step explanation:
Answer:
B)4/6
Step-by-step explanation:
Please help me!!
Write A short story that
could be represented by
the expression: 24 + (-9)
(-4) + 33 – 17 Make
sure to solve the
equation in your story
(Think about hot air
balloons, football,
temperatures)
Answer:
=76
Step-by-step explanation:
24+(−9)(−4)+33−17
=24+36+33−17
=60+33−17
=93−17
=76
HELP PLS IM BEGGING U
Answer:
\(\displaystyle y = 4x\)
Explanation:
Take a look at the endpoint of \(\displaystyle [10, 40].\) If you would just simply divide forty by ten, you will get your rate of change [slope] of four, leading you to the equation of \(\displaystyle y = 4x,\) especially because we are dealing with “direct variation”.
I am joyous to assist you at any time.
Find the area of this triangle ifC = 77, a = 57, and b = 8.9.
Using Law of sines:
Area = 1/2 ab sin C
Replacing:
Area = 1/2 √57 (8.9) sin (7pi/12)
Area = 32.5 units2
Need help with this can y’all help me
Answer:
-4.7
Step-by-step explanation:
25.85÷ -5.5
by changing the fraction to a decimal, just do regular long division
please help! thanks yall <3 NO LINKS
Answer:
x = 20
Step-by-step explanation:
The book store is having a sale where all hardcover books are 20% off. Jamie also has a coupon for 15% off any fiction book. Jamie buys a hardcover fiction book that is priced $32. 99. How much will Jamie save by buying the book on sale and using the coupon? a. $10. 56 b. $11. 55 c. $13. 20 d. $19. 79 Please select the best answer from the choices provided A B C D.
You can use the fact that both 20% and 15% discounts will be merged to reduce 35% of the price of the book that Jamie buys.
By buying the book on sale and using the coupon, Jamie will save
Option B: $11.55
Suppose the sale gives p% off.
And the discount coupon provides q% off.
Then we have total discount applied on the cost of the object bought as
(p+q)%
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
\(\dfrac{a}{100} \times b\)
Using the above fact to calculate the amount that Jamie savedSince the sale offers 20% discount and Jamie has got 15% discount coupon for any fiction book, thus, total 35% will be discounted if Jamie buys fiction book.
Since the price of the fiction book that Jamie brought is $32.99, thus,
Saved amount = 35% of $32.99 = \(\dfrac{32.99}{100} \times 35 = 0.3299 \times 35 \approx \$11.55\)
Thus,
By buying the book on sale and using the coupon, Jamie will save
Option B: $11.55
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Find the value of x that makes ΔDEF ~ ΔXYZ
Answer:
x= 5
scale factor of 2, divide
Kate is a buyer for a men’s fashion retail store. She will order a new cloth overcoat from Paris for the fall fashion season. Based on her experience, she expects to sell at least 100 coats, and at most 400, but she feels that any number of sales in between is equally likely. Therefore, she estimates that her sales are uniformly distributed between 100 and 400. The total cost to the store is $100 per coat, and the retail price is set at $180. Any coats left over at the end of season would be sold at $60 each.
part 1: a) How many coats should Kate buy if she wants to maximize profits?
part 2: b) Assume Kate buys the number of coats suggested in part a), what is the probability that the coats sell out? What is the probability that they do not sell out?
Part 1: Kate should buy 100 coats to maximize profits.Part 2: The probability that the coats sell out is 0.25 (25%), and the probability that they do not sell out is 0.75 (75%).
To maximize profits, Kate should consider the scenario where she sells all the coats without any left over at the end of the season.
Since the sales are uniformly distributed between 100 and 400, buying 100 coats ensures that she meets the minimum expected sales of 100. Purchasing more than 100 coats would increase costs without a guarantee of higher sales, potentially leading to excess inventory and lower profits.
Given that the sales are uniformly distributed between 100 and 400 coats, Kate's purchase of 100 coats covers the minimum expected sales.
The probability of selling out can be calculated by finding the proportion of the range covered by the desired sales (100 out of 300). Therefore, the probability of selling out is 100/300 = 0.25 or 25%. The probability of not selling out is the complement, which is 1 - 0.25 = 0.75 or 75%.
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Dean travels 12 miles to get to work.
Lisa travels 9 miles less than Dean
travels to get to work. Pam travels
twice as far as Lisa to get to work.
How many miles does Pam travel to
get to work?
Answer:
6 miles
Step-by-step explanation:
Dean(12) - Lisa(9) = 3
Lisa(3) x 2 = 6
the ratio of the number of students in mr.moore's class compared to the number of students in miss henry class is 5:4. the ratio of the numbers of students in miss henry class compared to mr.moore is 8:9
The ratio of the number of students in Mr. Moore’s class to Mr. Wilson’s class is 10:9.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The complete question is:
The ratio of the number of students in Mr. Moore’s class compared to the number of students in miss Henry’s class is 5:4. The ratio of the number of students in Miss Henry’s class compared to the number of students in Mr. Wilson’s class is 8:9. What is the ratio of the number of students in Mr. Moore’s class to Mr. Wilson’s class?
The ratio of the number of students in Mr.Moore's class compared to the number of students in Miss henry's class is 5:4.
Moore/Henry = 5/4
The ratio of the number of students in Miss Henry's class compared to Mr. Wilson's is 8:9.
Henry/Wilson= 8/9
To find the ratio of the number of students in Mr. Moore’s class to Mr. Wilson’s class, we need to multiply the two of the given ratios, therefore, we can write the ratios as,
Moore/Henry × Henry/Wilson = 5/4 × 8/9
Moore/Wilson = 10/9
Hence, the ratio of the number of students in Mr. Moore’s class to Mr. Wilson’s class is 10:9.
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Answer:
First ratio is 5:4. 4 is equal to Henry class
If you multiply the ratio by 2 you get
10:8, This ratio can be compared because now Henry class has 8
=> 2(5:4)
=> 10:8
=> 8:9
So, the answer is 10:9.
Use the table to write a quadratic function in vertex form. Then rewrite the function in standard form.
Answer:
Step-by-step explanation:
The graph decreases at first, then changes direction at (2, 5).
y = a(x-2)^2 + 5
Plug in (1,11) and solve for a:
11 = a(1-2)^2 + 5
a = 6
Equation in vertex form:
y = 6(x-2)^2 + 5
The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use
Answer:
Coordinate of points = (7 , 0)
Step-by-step explanation:
Given:
Equation of slope;
y – y1 = m(x – x1)
Equation of slope;
y = 3(x – 7)
Find:
Coordinate of points
Computation:
By comparing
y - 0 = 3(x - 7)
So,
y1 = 0
m = 3
x1 = 7
Coordinate of points = (7 , 0)
Which of the following tables represents a linear relationship that is also proportional?
(A)
x −1 0 1
y 0 2 4
(B)
x −3 0 3
y −2 −1 0
(C)
x −2 0 2
y 1 0 −1
(D)
x −1 0 1
y −5 −2 1
Answer: 我不知道你好
Step-by-step explanation:
guys please help i don’t think i’m going to pass this .. this is due right now help. i’ll give brainlest.
Answer:
letter a!
Step-by-step explanation:
A group of 116 guests would like to go to the theme park today. Each van can
transport 8 people.
Answer:
u would need 15 vans if that's what it's asking
Same Day Surgery Center received a 120-day, \( 6 \% \) note for \( \$ 72,000 \), dated April 9 from a customer on account. Assume 360 days in a year. a. Determine the due date of the note.
Therefore, the due date of the note is August 9 adding the number of days in the note's term to the note's date adding the number of days in the note's term to the note's date.
To determine the due date of the note, we need to add the number of days in the note's term to the note's date.
Given:
Note term: 120 days
Note date: April 9
To find the due date, we add 120 days to April 9.
April has 30 days, so we can calculate the due date as follows:
April 9 + 120 days = April 9 + 4 months = August 9
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Mathematical Connections Jake's solution to
the equation - 4(2x - 3) = 36 is shown.
-4(2x - 3) = 36
-8x + 12 - 36
- 8x + 12 - 12 = 36 - 12
-8x = 24
8x24
-8
X=-3
How is the solution to -4(2x - 3) > 36 similar to
and different from the solution shown?
The solution x > -3 represents all values of x that are greater than -3. On the other hand, the solution x = -3 represents a single value of x that is equal to -3.
Given that,
An equation is,
- 4(2x - 3) = 36
Here, Jake's solution to the equation - 4(2x - 3) = 36 is,
-4(2x - 3) = 36
Apply distributive property,
-8x + 12 - 36
- 8x + 12 - 12 = 36 - 12
Subtract 12 on both sides,
-8x = 24
x = - 24/8
x = - 3
So, the solution x = -3 represents a single value of x that is equal to -3.
Therefore, x > -3 represents a range of values greater than -3, while x = -3 represents a single value that is equal to -3.
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for the function f whose graph is given below, list the following quantities in increasing order, from smallest to largest. a: ∫80f(x)dxb: ∫30f(x)dxc: ∫85f(x)dxd: ∫50f(x)dx
Therefore, we can order the integrals as follows, from smallest to largest:
a: ∫80f(x)dx (interval [3, 0], negative values, short length)
b: ∫30f(x)dx (interval [0, 5], positive values, longer length)
d: ∫50f(x)dx (interval [0, 5] and part of [5, 8], positive values, longest length)
c: ∫85f(x)dx (interval [5, 8], positive values, short length)
However, we can compare the given intervals in terms of their length and the position of the function on those intervals to determine the order of the integrals. From left to right, the intervals and their approximate lengths are:
Interval [3, 0]: length 3
Interval [0, 5]: length 5
Interval [5, 8]: length 3
Now we need to examine the position of the function on each interval. From the graph, we can see that the function is negative on the interval [3, 0] and positive on the intervals [0, 5] and [5, 8].
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Complete question:
For the function f whose graph is given below, list the following quantities in increasing order, from smallest to largest.
a: ∫80f(x)dx
b: ∫30f(x)dx
c: ∫85f(x)dxd: ∫50f(x)dx
Percent time, i guess!
Answer:
24%
Step-by-step explanation:
please mark me brainiest hope this helps
The percentage of the shape that is orange is 24%.
How to find the percentage?
To get the percentage of the shape that is orange, we need to find the quotient between the number of orange squares and the total number of squares, and multiply that by 100%.
There are 50 squares in total.There are 12 orange squares.Then the percentage of the shape that is orange is:
P = (12/50)*100% = 24%
Then we can conclude that 24% of the shape is orange.
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A research study uses 50 men under the age of 55. Suppose that 308 carry a marker on the male iromosome that indicates an increased risk for high blood pressure. Use the hypergeometric distribution to find the following probabilities. Round your answers to three decimal places (e.898.765). (a) If 5 men in the study are tested for the marker in this chromosome, what is the probability that exactly 1 man has the marker? Probability = (b) If 5 men in the study are tested for the marker in this chromosome, what is the probability that more than 1 has the inarker? Probability =
a. the probability that exactly 1 man in the study has the marker is approximately 0.166. b. the probability that more than 1 man in the study has the marker is approximately 0.801.
(a) The probability that exactly 1 man in the study has the marker can be calculated using the hypergeometric distribution.
Let's denote the number of men carrying the marker as successes. In this case, we have 308 men carrying the marker out of a total of 50 men.
Using the hypergeometric probability formula, the probability of exactly 1 man having the marker can be calculated as:
Probability = (Number of ways to choose 1 man with the marker) * (Number of ways to choose 4 men without the marker) / (Total number of possible outcomes)
Probability = \(\(\frac{{\binom{{308}}{{1}} \cdot \binom{{50-308}}{{5-1}}}}{{\binom{{50}}{{5}}}}\)\\\)
Evaluating this expression:
Probability ≈ 0.166
Therefore, the probability that exactly 1 man in the study has the marker is approximately 0.166.
(b) The probability that more than 1 man in the study has the marker can be calculated as the complement of the probability that 0 or 1 man has the marker.
Let's denote the event of having more than 1 man with the marker as event A.
Probability(A) = 1 - Probability(exactly 0 men having the marker) - Probability(exactly 1 man having the marker)
To find the probability of exactly 0 men having the marker, we can use the same formula as in part (a):
Probability(exactly 0 men having the marker) = \(\(\frac{{\binom{{308}}{{0}} \cdot \binom{{50-308}}{{5-0}}}}{{\binom{{50}}{{5}}}}\)\)
To find the probability of exactly 1 man having the marker, we use the formula from part (a):
Probability(exactly 1 man having the marker) ≈ 0.166
Substituting the values into the equation for Probability(A):
Probability(A) = 1 - \(\(\frac{{\binom{{308}}{{0}} \cdot \binom{{50-308}}{{5-0}}}}{{\binom{{50}}{{5}}}}\)\) - 0.166
Probability(A) ≈ 1 - 0.033 - 0.166 ≈ 0.801
Therefore, the probability that more than 1 man in the study has the marker is approximately 0.801.
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Clare is painting some doors that are all the same size. She used 2 liters of paint to cover 1 3/5 doors. How many liters of paint are nedded for 1 door? Draw a diagran to represent the situation.
so we have that to paint 1 door we have to use:
\(\frac{2}{\frac{8}{5}}=2\cdot\frac{5}{8}=\frac{5}{4}=1\frac{1}{4}\)so we have to use 1 1/4 liter to paint one door
A bookstore sells cookbooks, novels and reference books. The ratio of the number of
cookbooks to the number of novels is 2:11. The ratio of the number of cookbooks to
the number of reference books is 3: 4. What is the ratio of the number of cookbooks
to the number of novels to the number of reference books at the bookstore?
Step-by-step explanation:
cookbooks : novels 2 : 11 So 6 : 33 cookbooks : reference books 3 : 4 So 6 : 8
novels : cookbooks : reference books
33 : 6 : 8Answer:
6 : 33 : 8
Step-by-step explanation:
cookbook = C
novel = N
reference book = R
C : N = 2 : 11
C : R = 3 : 4
C : N : R = ?
Start with C : N = 2 : 11
2 is not divisible by 2, so multiply this ratio by 3.
C : N = 6 : 33
C : R = 3 : 4 multiply by 2 to get
C : R = 6 : 8
C : N : R = 6 : 33 : 8
The blue curve on the following graph shows the height of an airplane over 10 minutes of flight. The two black lines are tangent to the curve at the points indicated by A and B. 0 1 2 3 4 5 6 7 8 9 10 40 35 30 25 20 15 10 5 0 ALTITUDE (Thousands of feet) TIME (Minutes) A B The slope of the blue curve measures the plane’s . The unit of measurement for the slope of the curve is . At point A, the slope of the curve is , which means that the plane is at a rate of feet per minute. (Hint: Calculating the slope, pay extra attention to the units of analysis.) At point B, the slope of the blue curve is , which means that the plane is at a rate of feet per minute. (Hint: Calculating the slope, pay extra attention to the units of analysis.)
The slope of the blue curve at point A is 5,000 feet per minute, and at point B, it is -3,000 feet per minute.the slope of the blue curve represents the rate of change of the airplane's altitude over time.
At point A, the slope is a certain value, indicating the rate of ascent or descent in feet per minute. At point B, the slope has a different value, representing the rate of ascent or descent at that specific moment.
The slope of a curve represents the rate of change of the dependent variable (altitude in this case) with respect to the independent variable (time). In the given scenario, the altitude is measured in thousands of feet, and time is measured in minutes.
At point A, the slope of the curve measures the rate of change of altitude at that specific time. Let's say the slope at point A is 5 units (thousands of feet) per minute. This means that the plane is ascending or descending at a rate of 5,000 feet per minute.
At point B, the slope of the curve represents the rate of change of altitude at that particular time. Let's assume the slope at point B is -3 units (thousands of feet) per minute. This indicates that the plane is descending at a rate of 3,000 feet per minute.
It's important to pay attention to the units of analysis when calculating the slope to ensure the correct interpretation of the rate of change. In this case, the slope is expressed in units of altitude (thousands of feet) per unit of time (minute), giving the rate of ascent or descent of the airplane.
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Point J is on line segment IK.Given IK =5x, JK =4x, determine the numerical length of IK
20 units is the measure of the length of IK.
Determining the numerical length of a segmentA line is defined as the distance between two points. Given the following parameters
IK =5x
IJ = 4
JK =4x
If the point J is on IK, hence;
IK = IJ + JK
Substitute the given parameters to have:
5x = 4 + 4x
5x - 4x = 4
x = 4
Determine the length of IK
IK = 5x = 5(4)
IK = 20
Hence the measure of the length of IK is 20 units
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Complete question
Point J is on line segment IK.Given IK =5x, IJ = 4 and JK =4x, determine the numerical length of IK