Answer:
1/4, 0.25
13/40, 0.325
1/25, 0.04
3/4, 0.75
13/200, 0.065
1 1/4, 1.25
1/8, 0.125
1/500, 0.002
3/400, 0.0075
107/100, 1.07
21/10, 2.10
9/40, 0.225
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
(0.020(5/4) + 3 ((1/5) – (1/4)))
Answer:
- 0.125
Step-by-step explanation:
Given the equation :
(0.020(5/4) + 3 ((1/5) – (1/4)))
0.020(5/4) = 0.025
3((1/5) - (1/4)) = 3(1/5 - 1/4) = 3(-0.05) = - 0.15
0.025 + - 0.15 = 0.025 - 0.15 = - 0.125
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.
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.
At the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 cheeses
Answer:
Diego can choose the 15 items in 128 different ways.
Step-by-step explanation:
Since at the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads, and he wants to use the Express Lane, so he can only buy 15 items, to determine how many ways can he choose which 15 items to buy if he wants all 6 cheeses the following calculation must be performed:
4 x 4 x 8 = X
16 x 8 = X
128 = X
Therefore, Diego can choose the 15 items in 128 different ways.
help please quick please
Answer:
the answer is 3.5
Step-by-step explanation:
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
convert 6 miles to meters
Answer:
9656.06 meters
Step-by-step explanation:
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.
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
Solve the inequality 5u≤8u−21 and write the solution in interval notation
Answer:
Step-by-step explanation:
[tex]5u\leq 8u-21[/tex]
Subtract 8u from both sides
[tex]-3u\leq -21[/tex]
Divide by -3 on both sides
[tex]u\geq 7[/tex]
Interval notation: [greater/less than or equal to], (greater or equal to)
[7,∞)
The solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).
What is inequality?In mathematics, an inequality is a remark that two values or expressions are not equal. An inequality uses one of the comparison symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).
Here,
To solve the inequality 5u ≤ 8u - 21, we can start by isolating u on one side of the inequality. We can do this by subtracting 5u from both sides:
5u ≤ 8u - 21
-3u ≤ -21
Divide both sides by -3. Note that dividing by a negative number will reverse the direction of the inequality:
u ≥ 7
Therefore, the solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).
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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.
How can I describe an angle's measure?
Recounting Rectangles
How many rectangles are
there in the figure below?
Answer:
gimme a second, I'll comment
Write the word sentence as an inequality.
3.2 less than a number t is at most 7.5
t-3.2 ≤ 7.5
"at most" means less than or equal to
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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The in center is the center of the circle of a triangle
1) circumscribed
2) centralized
3) cocentric
4) inscribed
Answer:
inscribed
Step-by-step explanation:
For any given triangle, the circle inside of it is called the Inscribed circle
61 1/20 as a decimal
Answer:
61.05
Step-by-step explanation:
1/20 = 5/100 = 0.05
61+0.05 = 61.05
Which inequality is true?
А. Зп > 9
B. 7 + 8< 11
C. 27 -1 < 5
D. 2 > 2
SUBMIT
< PREVIOUS
9514 1404 393
Answer:
А. Зп > 9
Step-by-step explanation:
The inequality of A may or may not be true. (It is true only if n > 3.) All of the others are definitely false.
Alexander is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.
Over one month, he collected 1297 cans.
What is the mass, in kilograms, of these cans?
Answer:
22 kg
Step-by-step explanation:
1297 cans * (17 grams)/(1 can) * (1 kg)/(1000 g) = 22.049 kg
Answer: 22 kg
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
Hello please help me solve this inequality shown in the graph, thank you so much!
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
Olivia randomly samples 50 students attending a basketball game and asks what grade they are in. Of the studets surveyed, 19 were in the seventh grade. I
there are 200 students attending the basketball game, based on the sample, how many of them are in seventh grade?
Answer:
76
Step-by-step explanation:
19 out of 50 are in 7th grade.
200/50 = 4
Multiply both numbers in the ratio by 4.
19 out of 50 = 76 out of 200
Answer: 76
ASAP! see the picture please!!
Answer:
the second one
function A has a slope of 3
function B has a slope of 5
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
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.
For numbers 6-10, how long does it take to travel:
11. A car travels 200 kilometers in 8 hours. Calculate the average speed of the car in:
a. Kilometer per hour
b. Kilometers per minute
This question have no choices specify your answers only
Answer:
A
Step-by-step explanation:
You divide distance over time so 200 divided by 8.
evaluate the expression when f=6 12f+3
Answer:
75
Step-by-step explanation:
Substitute 6 for f
12f+3=
12*6+3=
72 + 3 = 75
Answer:
12f+3 = 75 when f = 6
Step-by-step explanation:
12f+3
Let f = 6
12*6+3
Multiply
72 +3
Add
75
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
