9514 1404 393
Answer:
152
Step-by-step explanation:
The third one is their average, so is 740/5 = 148. The largest is 4 more than that, so ...
the largest value of the group is 152
_____
The numbers are 144, 146, 148, 150, 152.
The largest number when sum of five consecutive even integers is 740 is 152.
What is consecutive numbers?Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.
Example: 1,2,3,4,5,6
1,3,5,7,9,11
2,4,6,8,10,12
Difference between nearer numbers always equal
Given,
There are 5 consecutive even integers.
Then difference between each nearer number is 2
Let the first number be x
Then another 4 numbers be
(x + 2), (x + 4), (x + 6), (x + 8)
Now
According to question
(x + x + 2 + x + 4 + x + 6 + x + 8) = 740
5x = 740 - 20
x = 144
And the highest number is x + 8 = 152
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PLEASE HELP ME!!! I need to simplify these equations, not answer them.
Answer:
Step-by-step explanation:
a= 2qr^3 quotent 6p^2
what is the slope of the line that passes through these two points?
Answer:
slope of the line is 0
Step-by-step explanation:
given points are:
(-3 , 2)=(x1 , y1)
(4 , 2)=(x2 , y2)
slope =y2 - y1/x2 - x1
=2-2/4-(-3)
=0/4+3
=0/7
=0
Political party affiliation is believed to be a very strong indicator of how voters will vote in Presidential Elections. You are interested in determining if voter party loyalty has changed since 1992. During the 1992 election, the proportion of self-proclaimed Republicans who voted for George H. W. Bush was 0.924. During the 2012 election, in a survey of 277 Republican voters, 213 indicated that they had voted for Mitt Romney. The 90% confidence interval for this proportion is ( 0.7273 , 0.8106 ). What is the best conclusion you can make from this information that is listed below
Answer:
The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
In this question:
The 90% confidence interval for the proportion of Republican voters that had voted for Mitt Romney is (0.7273, 0.8106). The best conclusion is that we are 90% that the true population proportion of Republicans that voted for Mitt Romney is between 0.7273 and 0.8106.
Is this the correct answer?
Answer:
Correct.
Step-by-step explanation:
It looks good to me.
Good job!
61 1/20 as a decimal
Answer:
61.05
Step-by-step explanation:
1/20 = 5/100 = 0.05
61+0.05 = 61.05
The pyramid shown below has a square base, a height of 7, and a volume of 84 cubic units.
What is the length of the side of the base?
12
36
6
18
The retail cost of a TV is 50 % more than its wholesale cost. Therefore, the retail cost is ____ times the wholesale cost.
Answer:
Let the retail cost be x and the wholesale cost be y
Step-by-step explanation:
x = y + 0.50y
x = 1.50y
Therefore the retail cost is 1.50 times the wholesale cost.
Find the length of the third side. If necessary, round to the nearest tenth.
Answer: 14.4
Step-by-step explanation:
Complete the explanation on why it is a good idea to use multiple samples when making comparative inferences about two populations.
It is a good idea to use multiple random samples to see how statistical measure vary among the ————-(different/same) samples.
What did she do wrong ?
Answer:
She wrongly added the equations
Step-by-step explanation:
Given
[tex]-3x + y = 8[/tex]
[tex]-3x + y = -4[/tex]
Required
Her mistake
The mistake is when she added the equations.
When both equations are added, the result is:
[tex]-3x -3x + y+y=8-4[/tex]
[tex]-6x +2y=4[/tex]
and not
[tex]2y = 4[/tex]
The suggestion to avoid such mistake is for the student to check the appropriate signs of each term before adding/subtracting.
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s. At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
Answer:
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Step-by-step explanation:
Volume of a right circular cone:
The volume of a right circular cone, with radius r and height h, is given by the following formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Implicit derivation:
To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
Radius is 107 in. and the height is 151 in.
This means that [tex]r = 107, h = 151[/tex]
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.
This means that [tex]\frac{dr}{dt} = 1.1, \frac{dh}{dt} = -2.6[/tex]
At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
This is [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}(2(107)(151)(1.1) + (107)^2(-2.6))[/tex]
[tex]\frac{dV}{dt} = \frac{2(107)(151)(1.1) - (107)^2(2.6)}{3}[/tex]
[tex]\frac{dV}{dt} = 1926[/tex]
Positive, so increasing.
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Let f(x)=x2+10x+37 .
What is the vertex form off(x)?
What is the minimum value off(x)?
Enter your answers in the boxes.
Vertex form: f(x)=
Minimum value of f(x):
Answer:
f(x) = (x+5)^2 +12
The minimum value is 12
Step-by-step explanation:
f(x)=x^2+10x+37
The vertex will be the minimum value since this is an upwards opening parabola
Completing the square by taking the coefficient of x and squaring it adding it and subtracting it
f(x) = x^2+10x + (10/2) ^2 - (10/2) ^2+37
f(x) = ( x^2 +10x +25) -25+37
= ( x+5) ^2+12
Th is in vertex form y = ( x-h)^2 +k where (h,k) is the vertex
The vertex is (-5,12)
The minimum is the y value or 12
How do i do this math equasion?
Answer:
f(t) = -16t² + 36
Step-by-step explanation:
f(t) = a(t - h)² + k
This is vertex form where (h, k) is the (x, y) coordinate of the vertex
The vertex is give as (0, 36)
f(t) = a(t - 0)^2 + 36
f(t) =at² + 36
use point (1, 20) to find "a"
20 = a(1²) + 36
20 = a + 36
-16 = a
f(t) = -16t² + 36
Kern Shipping Inc. has a requirement that all packages must be such that the combined length plus the girth (the perimeter of the cross section) cannot exceed 99 inches. Your goal is to find the package of maximum volume that can be sent by Kern Shipping. Assume that the base is a square.
a. Write the restriction and objective formulas in terms of x and y. Clearly label each.
b. Use the two formulas from part (a) to write volume as a function of x, V(x). Show all steps.
Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]
[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]
⇒ 198x - 12x² = 0
[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]
By solving for x:
x = 0 or x = [tex]\dfrac{33}{2}[/tex]
Again:
V = 99x² - 4x³
[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]
At x = [tex]\dfrac{33}{2}[/tex]
[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]
[tex]\implies 198 - 12 \times 33[/tex]
= -198
Thus, at maximum value;
[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]
Recall y = 99 - 4x
when at maximum x = [tex]\dfrac{33}{2}[/tex]
[tex]y = 99 - 4(\dfrac{33}{2})[/tex]
y = 33
Finally; the volume V = x² y is;
[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]
[tex]V =272.25 \times 33[/tex]
V = 8984.25 inches³
Solve the equation for w 5(w-2)+10=2w+6
Answer:
w=2
Step-by-step explanation:
See image below:)
Answer:
w = 1/2 or w = 3/6
Step-by-step explanation:
5(w-2) + 10 = 2w + 6
5(w-2) + 10 = 5w + 10 - 10 = 5w (the 5 outside of the bracket multiplies with the digits inside, including the w)
Now you have : 5w = 2w+6
Transfer the 2w to the left side, which would make it negative, therefore
5w - 2w= 6
3w = 6
w = 3/6
or
w = 1/2 (simplified)
ASAP! see the picture please!!
Answer:
the second one
function A has a slope of 3
function B has a slope of 5
Do the following lengths form a right triangle?
Answer:
Yes, they do
Step-by-step explanation:
Because
6+8=14>9
6+9=15>8
8+9=17>6
Abigail loves collecting stamps. A particular pack of stamps costs a lot of money, so she sells half of her collection in order to afford it. She buys the pack of 15 stamps and now has 145 total . How many did she have before she sold half of the collection?
Answer:
260
Step-by-step explanation:
145-15=130
130 x 2 = 260
Use the substitution method or the elimination method to solve the following system.
2x−20y
=
10
−7x+70y
=
−35
9514 1404 393
Answer:
x -10y = 5 . . . . . infinite number of solutions
Step-by-step explanation:
We can put each equation into standard form by dividing it by its x-coefficient.
x -10y = 5 . . . . first equation
x -10y = 5 . . . . second equation
Subtracting the second equation from the first eliminates the x-variable to give ...
(x -10y) -(x -10y) = (5) -(5)
0 = 0 . . . . . . . true for all values of x or y
The system has an infinite number of solutions. Each is a solution to ...
x -10y = 5.
33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
[tex] {x}^{2} + \sqrt{x} + \sqrt[5]{x} [/tex]
what is f'(3) of this equation?
Answer:
[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
Step-by-step explanation:
Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex] This way we could more easily use the power rule of derivatives.
So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.
f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]
to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
Find the area of each triangle
8 yd
8 yd
Answer:
Area of triangles 1 = 18 ft²
Area of triangles 2 = 16 in²
Area of triangles 3 = 90 yd²
Step-by-step explanation:
Given:
1] Height of triangle = 4 ft
Base of triangle = 9 ft
2] Height of triangle = 4 in
Base of triangle = 8 in
3] Height of triangle = 12 yd
Base of triangle = 15 yd
Find:
Area of triangles
Computation:
Area of triangles = (1/2)(Base)(Height)
Area of triangles 1 = (1/2)(4)(9)
Area of triangles 1 = 18 ft²
Area of triangles 2 = (1/2)(4)(8)
Area of triangles 2 = 16 in²
Area of triangles 3 = (1/2)(12)(15)
Area of triangles 3 = 90 yd²
I’ll mark brainliest
Answer:
[tex]\text{A. }y=1.30x+1.50[/tex]
Step-by-step explanation:
The two ringtones will cost her a total of [tex]0.75\cdot 2=1.50[/tex] and is a fixed amount. The relationship between the cost and number of songs only is [tex]y=1.30x[/tex] and therefore the answer is [tex]\boxed{\text{A. }y=1.30x+1.50}[/tex]. You can also directly find the answer by finding the y-intercept (in this case [tex]1.50[/tex]), as no other answer choices include the term [tex]1.50[/tex], so A must be the correct answer.
What is the slope and y-intercept of 6x-5y=13
Answer:
The slope is 6/5 and the y intercept is -13/5
Step-by-step explanation:
6x-5y=13
Solve for y
Subtract 6x from each side
6x-6x-5y=-6x+13
-5y = -6x+13
Divide by -5
-5y/-5 = -6x/-5 +13/-5
y = +6/5x -13/5
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
The slope is 6/5 and the y intercept is -13/5
Which of the following values could be an absolute value?
Answer:
Step-by-step explanation: It could be 8,7, or 2. Because these are all positive
:)
Solve for z
3z-5+2z=25-5z
Answer:
z=3
Step-by-step explanation:
1. collect like terms
5z-5=25-5z
2. Move the variable to the left hand side and change its sign
5z-5+5z=25
3. Collect like terms
10z=25+5
4. Divide both sides of the equation by 10
z=3
The solution to the equation is z = 3.
To solve for z in the equation 3z - 5 + 2z = 25 - 5z, we can simplify and combine like terms on both sides:
3z + 2z + 5z = 25 + 5
Combining the terms on the left side gives:
10z = 30
Next, we isolate the variable z by dividing both sides of the equation by 10:
(10z)/10 = 30/10
This simplifies to:
z = 3
Therefore, the solution to the equation is z = 3.
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explain how to write an equation of a line given the slope and one point on the line
please help now
Your pump empties the water from a swimming pool in 4 hours. When your friend's pump is used together with your pump, the pool is emptied in 48 minutes. How long (in hours) does it take your friend's pump to empty the pool when working alone?
Answer:
Time taken for pump B to empty pool = 1 hour.
Step-by-step explanation:
Given:
Time taken for pump A to empty pool = 4 hour
Time taken together = 48 minutes = 48 / 60 = 4/5 hour
Find:
Time taken for pump B to empty pool
Computation:
Assume;
Time taken for pump B to empty pool = a
1/4 + 1/a = 1 / (4/5)
1/4 + 1/a = 5/4
1/a = 5/4 - 1/4
1/a = (5 - 1) / 4
1/a = 1
a = 1
Time taken for pump B to empty pool = 1 hour.
Please help a girl out, math is not my forte
Answer:
80 ft²
Step-by-step explanation:
You are given the formula
a = (1/2)bh
Just plug in the base and height, then multiply
a = (1/2) * 8 *20
a = (1/2) * 160
a = 80 ft²
Answer:
80 [tex]ft^{2}[/tex]
Step-by-step explanation:
Area = [tex]\frac{1}{2} bh[/tex]
Area = [tex]\frac{1}{2}[/tex] 8 · 20
Area = [tex]\frac{1}{2}[/tex] 160
Area = 80 [tex]ft^{2}[/tex]
Use the order of operations to simplify the expression
(5.4)² - 5.4²
Answer:
0
Step-by-step explanation:
(5.4)^2 - 5.4^2
= 5.4^2 - 5.4^2
= 5,4^2(1 - 1)
= 5.4^2(0)
= 0
