Answer:
7
Step-by-step explanation:
Q1 = 14
Q3 = 21
Take 21 - 14 and it gives you the interquartile range of 7.
Final answer:
The interquartile range (IQR) for the data set with a five-number summary of 10, 14, 15.5, 21, 25 is 7, calculated as the difference between the third quartile (Q3) and the first quartile (Q1), which are 21 and 14 respectively.
Explanation:
The interquartile range (IQR) of a data set is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Given the five-number summary of 10, 14, 15.5, 21, 25, where 14 is Q1 and 21 is Q3, the IQR can be found using the formula:
IQR = Q3 - Q1
In this case:
IQR = 21 - 14
IQR = 7
Therefore, the interquartile range for this data set is 7.
Please answer ASAP! Thank you in advance and make sure to use antibacterial soap and wash your hands for 1 minute.
Answer:
[tex]12.5 \ ft^2[/tex]
Step-by-step explanation:
Given that height is a quarter the sum of bases and that the height is 2.5ft.
The sum of bases is calculated as:
[tex]h=\frac{1}{4}\sum{b_i}=2.5\\\\\sum{b_i}=2.5\times 4\\\\\sum{b_i}=b_1+b_2=10\ ft[/tex]
#Having that (b1+b2=10 ft), we can now calculate the area using the given formula using the given figures:
[tex]A=\frac{1}{2}\times 2.5\times (b_1+b_2), b_1+b_2=10\\\\=\frac{1}{2}\times 2.5\times10\\\\=12.5[/tex]
Hence, the area of the trapezoid is 12.5 sq ft
*Using the h=2.5ft and the [tex]A=\frac{1}{2}h(b_1+b_2)[/tex]
flagpole casts a shadow that is 50 feet long. At the same time, a woman who is five feet four inches tall casts a shadow 40 inches long. How tall is the flagpole
Answer:
960 in (or 80 ft)
Step-by-step explanation:
First, we should convert all of the feet measurements to inches so we have equal units of measurements:
50 ft = 600 in
5 ft 4 in = 64 in
40 in = 40 in
Now we can solve this problem with a simple proportion:
h / 600 = 64 / 40
600 * 64 = 40h
38400 = 40h
960 in = h
***also h = 80 ft
By setting up a proportion of corresponding sides from similar triangles, we find that the flagpole's height is roughly 80 feet.
Explanation:This is a problem of similar triangles. The flagpole and its shadow form one triangle, and the woman and her shadow form a smaller, similar triangle. Since the triangles are similar, the ratio of corresponding sides should be equal. In this case, we have:
height of the flagpole / shadow of the flagpole = height of the woman / shadow of the woman
We can plug the provided values into this equation:
height of the flagpole / 50 feet = 5.33 feet / 3.33 feet
To solve for the height of the flagpole, we cross-multiply and divide, giving us:
height of the flagpole = (5.33 feet / 3.33 feet) * 50 feet
Following that logic, the height of the flagpole is approximately 80 feet tall.
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A central angle of a sector equals 5 radians and the radius equals 20 inches. What is the measure of the arc length formed by the sector?
Answer:
100
Step-by-step explanation:
-6h+7=-17 what would h equal.
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
-6x__ should equal -17 so my best choice would to guess and check
if we do 5 that will give us -23 i believe
if we do 4 it gives us -17 so this would be our answer 4
Which is true regarding Adi's use of algebra tiles?
Adi used algebra tiles to represent the product
(-2x-2)(2x-1).
A. She used the algebra tiles correctly.
B. She did not represent the two original factors correctly
on the headers.
C. The signs on some of the products are incorrect.
D. Some of the products do not show the correct powers
of x.
Answer:
A. True
B. False
C. False
D. False
Step-by-step explanation:
Hence she used it correctly by making parts of it.
Answer: Its A my boy
Step-by-step explanation:
What’s 4(-8x+5)-(33x-26)=
Answer:
x = -6/65
Step-by-step explanation:
Perform the indicated multiplications: 4(-8x+5) - 1(33x-26), obtaining:
-32x + 20 - 33x + 26
Combining like terms, we get
-65x = 6, or
x = -6/65
Please answer and explain (surface area)
Answer:
475 cm^2
Step-by-step explanation:
Base: 6 × 17 = 102
Left-most face: 6 × 11 = 66
Top face: 6 × 20 = 120
Front/Back faces: 11 × 17 = 187
Add: 102 + 66 + 120 + 187 = 475
Ben is 12 years older than Ishaan.Ben and Ishaan first met two years ago.Three years ago,Ben was 4 times as old as Ishaan.
Ben is 19 and Ishaan is 7.
If 3 years ago Ben was 4 times the age of Ishann, their ages could have been any of the following:
1. Ben is 4 and Ishaan is 1
2. Ben is 8 and Ishaan is 2
3. Ben is 12 and Ishaan is 3
4. Ben is 16 and Ishaan is 4
And so on.
Next add 3 to both ages, to show current age.
1. Ben is 7 and Ishaan is 4
2. Ben is 11 and Ishaan is 5
3. Ben is 15 and Ishaan is 6
4. Ben is 19 and Ishaan is 7
Ben is currently 12 years older than Ishaan. To find the difference, take Ben's age and subtract Ishaan's age.
1. 7 - 4 = 3
2. 11 - 5 = 6
3. 15 - 6 = 9
4. 19 - 7 = 12
Thus meaning Ben is 19 and Ishaan is 7.
I hope this helps!
Two functions are combined resulting in the function j(x) = -3x^2+5.
Which operations applied to the specified functions could result in j(x)? Select three options.
-two linear functions by addition
-two quadratic functions by addition
-a linear function and a quadratic function by addition
-two linear functions by multiplication
-two quadratic functions by multiplication
To obtain j(x) = -3x²+5, we need to combine a linear function and a quadratic function. Three possible options are provided in the response.
Explanation:The function j(x) = -3x²+5 is a quadratic function. To obtain this function by combining two other functions, we can use a linear function and a quadratic function added together. This means that one of the functions will have a degree of 1 and the other will have a degree of 2. Here are three options that could result in j(x):
Quadratic function: 2x²-7x+5
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A small island has a roughly rectangular shape. It is 18.2 kilometers wide and 28.5 kilometers long. Rising water levels are reducing the width by 1.2% each year and the length by 0.8% each year.
Use the drop-down menus to choose or create functions to model:
A. The width of the island over time, w(t)
B. The length of the island over time, l(t)
C. The area of the island over time, a(t)
Answer:
Part A) [tex]W(t)=18.2(1.012)^t[/tex]
Part B) [tex]L(t)=28.5(1.008)^t[/tex]
Part C) [tex]A(t)=518.7(1.020096)^t[/tex]
Step-by-step explanation:
we know that
The equation of a exponential growth function is equal to
[tex]y=a(1+r)^x[/tex]
where
a is the initial value
r is the rate of change
Part A) Create functions to model :
The width of the island over time, w(t)
we have
[tex]W(t)=a(1+r)^t\\[/tex]
where
[tex]a=18.2\ km\\r=1.2\%=1.2/100=0.012[/tex]
substitute
[tex]W(t)=18.2(1+0.012)^t[/tex]
[tex]W(t)=18.2(1.012)^t[/tex]
Part B) Create functions to model :
The length of the island over time, l(t)
we have
[tex]L(t)=a(1+r)^t\\[/tex]
where
[tex]a=28.5\ km\\r=0.8\%=0.8/100=0.008[/tex]
substitute
[tex]L(t)=28.5(1+0.008)^t[/tex]
[tex]L(t)=28.5(1.008)^t[/tex]
Part C) Create functions to model :
The area of the island over time, a(t)
we have
[tex]W(t)=18.2(1.012)^t[/tex]
[tex]L(t)=28.5(1.008)^t[/tex]
Remember that the area of a rectangle is given by
[tex]A=LW[/tex]
substitute the given values
[tex]A(t)=(28.5(1.008)^t)(18.2(1.012)^t)[/tex]
[tex]A(t)=(28.5*18.2)(1.008*1.012)^t)[/tex]
[tex]A(t)=518.7(1.020096)^t[/tex]
Answer:
Here's the answer ;)
Ava washes 12 % windows in /hour. At this rate, how many windows can
she wash in one hour?
Answer:
She will wash 24% windows in one hour
Step-by-step explanation:
If Ava washes 12% windows in half hour
Since 2 half hours makes one hour
Therefore, 2 × 12% will be washed in one hour
That is, Ava will wash 24% windows in one hour
Coach Jericho recorded the number of shots made by the starters on the 6th grade and 8th grade boys’ basketball team during the season.
6th Grade 8th Grade
22, 15, 17, 18, 20 58, 58, 52, 55, 53
Which statement is true? Select two answers.
A.
The data spread for the 8th graders is greater than for the 6th graders.
B.
Both sets of data have the same mean.
C.
The data set distribution for the 6th grade players is skewed right.
D.
The mean for the 8th grade players is 3 times the mean for the 6th grade players.
E.
The data set distribution for the 8th grade players is symmetric.
Answer:
D. The mean for the 8th grade players is 3 times the mean for the 6th grade players. & E. The data set distribution for the 8th grade players is symmetric.
The sum of four times a first number and a second number is 68. If the first number is decreased by twice the second number the result is -1. Find the numbers.
The first number is 15 and the second number is 8.
Step-by-step explanation:
Let us assume,
First number be 'x'.Second number be 'y'.Given :
Sum of four times a first number and a second number is 68.
⇒ 4x + y = 68
⇒ y = 68-4x
If the first number is decreased by twice the second number the result is -1.
⇒ x - 2y = -1
Substitute y = 68-4x in the above equation.
⇒ x - 2(68-4x) = -1
⇒ x-136+8x = -1
⇒ 9x - 136 = -1
⇒ 9x = -1+136
⇒ x = 135/9
⇒ x = 15
The first number is 15.
The second number is y = 68-4x.
⇒ y = 68 - 4(15)
⇒ y = 68-60
⇒ y = 8
The second number is 8.
Use synthetic substitution to find f(2) and f(3).
1.f(x) = 3x^4 - 12x^3 - 12x^2 + 30x
2. Write the polynomial equation of degree 4 with leading coefficient 1 that has roots at -2, -1, 3, and 4.
Answer:
see explanation
Step-by-step explanation:
(1)
To obtain f(2) and f(3) substitute x = 2, x = 3 into f(x)
f(2) = 3([tex]2^{4}[/tex] ) - 12(2³) - 12(2²) + 30(2)
= 48 - 96 - 48 + 60 = - 36
f(3) = 3([tex]3^{4}[/tex] ) - 12(3³) - 12(3²) + 30(3)
= 243 - 324 - 108 + 90 = - 99
(2)
Given a polynomial with roots x = a, x = b, then
(x - a), (x - b) are the factors
and the polynomial is the product of the factors
Here the roots are x = - 2, x = - 1, x = 3 and x = 4, thus the factors are
(x + 2), (x + 1), (x - 3) and (x - 4)
The polynomial is the product of the factors, thus
f(x) = (x + 2)(x + 1)(x - 3)(x - 4) ← expand in pairs using FOIL
= (x² + 3x + 2)(x² - 7x + 12) ← distribute
= [tex]x^{4}[/tex] - 7x³ + 12x² + 3x³ - 21x² + 36x + 2x² - 14x + 24 ← collect like terms
= [tex]x^{4}[/tex] - 4x³ - 7x² + 22x + 24
What is the area of the frame around the picture?
Answer:
40s units²
Step-by-step explanation:
Area of frame = area of bigger rectangle - area of smaller one
Area of big rectangle = length × breadth
= 12 × 6s = 72s unit²
Area of smaller rectangle = length x breadth
= 8 × 4s = 32s units²
Area of frame = 72s - 32s
= 40s units²
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Eric bought apples and oranges for $7.75. He paid $2.35 for all the apples
and $0.45 for each orange. How many oranges did he buy?
Answer:
He bought 12 oranges.
Step-by-step explanation:
Key words: "ALL the apples" "EACH orange."
7.75-2.35= 5.4
5.4/0.45= 12
Answer:
He bought 12 oranges.
Step-by-step explanation:
Keywords: "ALL the apples" and "EACH orange."
7.75-2.35= 5.4
5.4/0.45= 12
Step-by-step explanation:
Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8 centimeters, and the length of A C is 6.9 centimeters.
Which expressions can be used to find m∠BAC? Select three options.
To find the measure of angle BAC in the given right triangle ABC, we can use the trigonometric function sine.
To find the measure of angle BAC in the given right triangle ABC, we can use the trigonometric function sine. The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we know that the length of the side opposite angle BAC is 6.9 centimeters and the length of the hypotenuse is 12 centimeters. Therefore, we can use the equation sin(BAC) = opposite/hypotenuse to find the measure of angle BAC.
sin(BAC) = 6.9/12
BAC ≈ sin-1(6.9/12)
Using a calculator, we can find that BAC ≈ 33.24°.
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Need the response for this please help
Answer: it is important to keep both side of the equation balance while solving because, an equality sign is used which means, the right hand side is equal to the left hand side, and if the equation isn't balance we won't be able to get the correct answer for the missing variable.
We use greater than (>), less than (<) and greater than and equal to=> and less than and equal to <=
Step-by-step explanation:
2. Henri and Talia are mixing paint for an art project. They mixed p liters of red paint,
0.6 liters of blue paint, and p-0.4 liters of white paint. They then divided the mixture
evenly into 2 jars. If each jar contains 2.4 liters of paint, how many liters of red paint did
they use? Type your numeric answer below.
Answer:
They used 2.3 liters of red paint
Step-by-step explanation:
Henri and Talia are mixing paint for an art project.
They mixed amount of red paint = p liters
They mixed amount of blue paint = 0.6 liters
They mixed amount of white paint = p-0.4 liters
Total amount of paint = p +0.6 +p - 0.4 = 2p+0.2
They then divided the mixture evenly into 2 jars.
Amount of paint in 1 jar = [tex]\frac{2p+0.2}{2}[/tex]
We are given that Each jar contains 2.4 liters of paint
So, [tex]\frac{2p+0.2}{2}=2.4[/tex]
[tex]2p+0.2=2.4 \times 2[/tex]
[tex]2p+0.2=4.8[/tex]
[tex]2p=4.8-0.2[/tex]
2p=4.6
[tex]p=\frac{4.6}{2}[/tex]
p=2.3
Hence They used 2.3 liters of red paint
The correct statement is the red paint they use is 2.3 liters.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
They mixed p liters of red paint, 0.6 liters of blue paint, and a p-0.4 liter of white paint.
They then divided the mixture evenly into 2 jars. If each jar contains 2.4 liters of paint.
How to find the red color in it?They mixed p liters of red paint, 0.6 liters of blue paint, and a p-0.4 liter of white paint. According to this, the total paint will be
The total paint in liters = p + 0.6 + p - 0.4
The total paint in liters = 2p + 0.2
They then divided the mixture evenly into 2 jars. If each jar contains 2.4 liters of paint. According to this,
[tex]\rm \dfrac{2p+0.2}{2} = 2.4[/tex]
On solving the equation, then p will be
[tex]\begin{aligned} \rm \dfrac{2p+0.2}{2} &= 2.4\\\rm 2p + 0.2 &= 4.8\\\rm 2p &= 4.6\\\rm p &= 2.3\end{aligned}[/tex]
Thus, 2.3 liters of red paint did they use.
More about the linear system link is given below.
something + something = 48
something * something = -40
Answer:
Hello there!
So, your question is
"something + something = 48"
and
"something * something = -40"
Since you didn't really give that much specific details, and you could correct me on this later, I'd say for the first one it's
47 + 1 = 48
As for the second one, it could be
-5 * 8 = - 40
OR
5 * -8 = -40
both ways are correct.
Step-by-step explanation:
Hope this helps! If you have more instructions on this question, please let me know! Instructions are very important for MATH, cause even I mess up if the instructions are not clear. :)
- immaback2x
Answer:
Hi
Step-by-step explanation:
Which is the best step to do next to solve the equation by
completing the square?
The first few steps in solving the quadratic equation 5x2 +
27x = 14 - 13x by completing the square are shown.
5x2 + 27x = 14 - 13x
5x2 + 40x = 14
5(x2 + 8x) = 14
5(x2 + 8x + 16) = 30
5(x2 + 8x + 16) = 94
5(x2 + 8x + 4) = 18
5(x2 + 8x + 4) = 34
Answer:The correct answer among the choices given is option 2.
Completing the square is done as follows:
1. Write the equation in a way that the constants are in the right side while the terms with x are on the left.
5x^2 + 27x + 13x = 14
5x^2 + 40x = 14
2. Make sure that the coefficient of the x^2 term is 1.
5(x^2 + 8x) = 14
3. Adding a term to both sides that will complete the square in the left side. This is done by dividing the coefficient of the x term by 2 and squaring it. Note: The same amount should be added to the right side to balance the equation.
5(x^2 + 8x + 16) = 14 + 80
5(x+4)^2=94
Step-by-step explanation:
The correct step is 5x2 + 40x = 14.
What is Completing the square method?Completing the square is a method that is used for converting a quadratic expression of the form ax^2 + bx + c to the vertex form a(x - h)2 + k.
The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)^2 + n, such that the left side is a perfect square trinomial. Completing the square method is useful in:
Converting a quadratic expression into vertex form.Analyzing at which point the quadratic expression has minimum/maximum value.Graphing a quadratic function.Solving a quadratic equation.Deriving the quadratic formula.Given:
5x^2 + 27x = 14 - 13x
5x^2 + 27x + 13x = 14
5x^2 + 40x = 14
5(x^2 + 8x) = 14
Now,
Adding a term to both sides that will complete the square in the left side.
by dividing the coefficient of the x term by 2 and squaring it.
5(x^2 + 8x + 16) = 14 + 80
5(x+4)^2=94
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Write an equation of the line that passes through a pair of points (5, -2) , (4,5)
Answer:
y = -7x + 33
Step-by-step explanation:
Use the Point Slope Form: (y - y1) = m(x - x1)
Step 1: Find the Slope
Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Slope = [tex]\frac{5 - (-2)}{4 - 5}[/tex]
Slope = [tex]\frac{5 + 2}{-1}[/tex]
Slope = [tex]\frac{7}{-1}[/tex]
Slope = -7
Step 2: Plug into the point slope form
(y - 5) = -7(x - 4)
y - 5 + 5 = -7x + 28 + 5
y = -7x + 33
Answer: y = -7x + 33
7. (03.05 LC)
The functions f(x) and g(x) are described below:
f(x) = 7x + 9
g(x) = 7x – 4
The graph of g(x) is obtained by shifting down the graph of f(x) byl
units. (5 points)
8. (03.05 LC)
T
halha
t atamata baze decrribae the Affert frankmino thaiarnik
r.
Answer:
13 units
Step-by-step explanation:
g(x) = 7x + 9 - 13
g(x) = f(x) - 13
Answer:
7. the answer is 13
Step-by-step explanation:
suppose you connect the points on the graph in the example, what would the graph look like?
Answer:
Your graph would look like lines going up and up and up
Step-by-step explanation:
Why you ask? Well, because the graph shown here is going by the factors of 6. And the factors of 6 are pretty high, which means it would be going up like a twisted line going right ot left depending which way you look at it. It would be going up and up because like 18 times 6 is 108 and 20 times 6 is 120.
HELP! PLEASE! Jackson is building a small rectangular basketball section in his backyard. The length of the section will be 1.25 times the width of the section.
Part A
Create an equation to represent the area of the basketball section, A, in terms of the width, w.
Part B
Jackson decides to make the area of the basketball section 245 square feet. What are the dimensions, in feet, of the basketball section?
SHOW ALL WORK PLEASE
Answer:
Part A) [tex]A=1.25W^2[/tex]
Part B) Length: 17.5 feet and Width: 14 feet
Step-by-step explanation:
Part A) Create an equation to represent the area of the basketball section A, in terms of the width W.
Let
L ----> the length of the rectangular basketball section
W ---> the width of the rectangular basketball section
we know that
The area of the rectangular basketball section is equal to
[tex]A=LW[/tex] ----> equation A
The length of the section will be 1.25 times the width of the section
so
[tex]L=1.25W[/tex] ----> equation B
substitute equation B in equation A
[tex]A=(1.25W)W\\A=1.25W^2[/tex]
Part B) Jackson decides to make the area of the basketball section 245 square feet. What are the dimensions, in feet, of the basketball section?
we have
[tex]A=1.25W^2\\A=245\ ft^2[/tex]
so
[tex]245=1.25W^2[/tex]
solve for W
[tex]W^2=245/1.25\\W^2=196\\W=14\ ft[/tex]
Find the value of L
substitute the value of W in the equation B
[tex]L=1.25(14)=17.5\ ft[/tex]
therefore
The dimensions are :
Length: 17.5 feet
Width: 14 feet
The area equation for the basketball section is A = 1.25w². For an area of 245 square feet, the width, w, is approximately 14 feet, and the length, l, is approximately 17.5 feet.
Explanation:Part A: Equation of the Area
To create an equation that represents the area, A, of the basketball section in terms of the width, w, we start with the fact that the length is 1.25 times the width. So, if l represents the length, then l = 1.25w. The area of a rectangle is found by multiplying the length by the width, hence the area A = l × w. Substituting l = 1.25w gives us the equation A = (1.25w) × w = 1.25w².
Part B: Dimensions of the Basketball Section
Given the area of the basketball section is 245 square feet, we can use the equation found in Part A to determine the width and subsequently the length. The equation A = 1.25w² becomes 245 = 1.25w². Solving for w, we take the square root of both sides after dividing by 1.25, which gives w = √(245/1.25) ≈ 14 feet. To find the length, l, we multiply the width by 1.25, resulting in l = 1.25 × 14 ≈ 17.5 feet. Therefore, the dimensions are approximately 14 feet in width and 17.5 feet in length.
Select the expression that represents the following statement: 52 minus 4 times the difference of 13 and 7.
Answer:
(52 - 4) * (13 - 7)
Step-by-step explanation:
Step 1: Convert words into an expression
52 minus 4 times the difference of 13 and 7.
(52 - 4) * (13 - 7)
Answer: (52 - 4) * (13 - 7)
If needed simplify
(52 - 4) * (13 - 7)
48 * 6
288
The circle is inscribed in triangle PRT. A circle is inscribed in triangle P R T. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T. The length of R S is 5, the length of P U is 8, and the length of U T is 6. Which statements about the figure are true? Select two options. The perimeter of the triangle is 19 units. TU ≅ TS PU ≅ TU The length of line segment PR is 13 units. The length of line segment TR is 10 units.
Option B: [tex]TU $\cong$ TS PU $\cong$ TU[/tex]
Option C: The length of line segment PR is 13 units.
Explanation:
Given that the circle is inscribed in triangle PRT. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T.
The length of RS is 5, the length of PU is 8 and the length of UT is 6.
Option A: The perimeter of the triangle is 19 units.
The perimeter of the triangle is given by
Perimeter of ΔPRT = PU + UT + TS + SR + RQ + QP
Since, P, T and R are tangents to the circle and we know that "Tangents to a circle drawn to a point outside the circle are equal in length".
Thus, we have,
RS = RQ = 5
PU = PQ = 8 and
UT = TS = 6
Substituting the values in the perimeter of ΔPRT, we get,
Perimeter of ΔPRT = 8 + 6 + 6 + 5 + 5 + 8 =38 units
Thus, the perimeter of the triangle is 38 units.
Hence, Option A is not the correct answer.
Option B : [tex]TU $\cong$ TS PU $\cong$ TU[/tex]
Since, P, T and R are tangents to the circle and we know that "Tangents to a circle drawn to a point outside the circle are equal in length".
Then [tex]TU $\cong$ TS PU $\cong$ TU[/tex]
Hence, Option B is the correct answer.
Option C: The length of line segment PR is 13 units.
The length of PR is given by
PR = PQ + QR
Substituting the values RQ = 5 and PQ = 8, we get,
PR = 5 + 8 = 13 units
Thus, the length of line segment PR is 13 units.
Hence, Option C is the correct answer.
Option D: The length of line segment TR is 10 units.
The length of TR is given by
TR = TS + SR
Substituting the values TS = 6 and SR = 5, we get,
TR = 6 + 5 = 11 units
Thus, the length of line segment TR is 11 units
Hence, Option D is not the correct answer.
Answer: b and e
Step-by-step explanation:
Factor the expression: 8t-32u
Answer:
Step-by-step explanation:
8t - 32u = 8*t - 8*4*u
= 8*(t - 4u) = 8(t -4u)
A chemist needs 500mL of 20% acid and 80% water mix for an experiment. He adds x mL of a 10% acid and 90% water and y mal of a 30% acid and 70% water mix to the 20% acid and 80% water mix. Find the amounts x and y
Answer:
x = y = 250 mL
Step-by-step explanation:
The desired concentration of acid (20%) is exactly halfway between the concentrations of the available supplies (10%, 30%). So, the mix will be equal parts of each of those. x and y are both half the total quantity required:
x = y = (500 mL)/2 = 250 mL
_____
If you need an equation to solve this, you can let x = 500 -y and write the equation for the acid volume in the final mix:
10%(500 -y) +30%(y) = 20%(500)
50 -0.1y +0.3y = 100 . . . . . eliminate parentheses
0.2y = 50 . . . . . . . . . . . . . . subtract 50, collect terms
y = 250 . . . . . . . . . . . . . . . multiply by 5 (equivalently, divide by 0.2)
x = 500 -250 = 250
it take 96 pounds or seed to completely plant a 10-acre field. how many pounds of seed are needed per acre?
Answer:
9.6 lb/acre
Step-by-step explanation:
This is a unit rate problem. You want to know the number of pounds used for one acre.
You divide 96 pounds by 10 acres to find the number of pounds per 1 acre.
(96 lb)/(10 acres) = 9.6 lb/acre
Answer: 9.6 lb/acre
To find how many pounds of seed are needed per acre, divide the total amount of seed used, which is 96 pounds, by the total area, 10 acres. The answer is 9.6 pounds per acre.
Explanation:This problem is a simple division problem in Mathematics. We start by taking the total amount of seed that was used, which is 96 pounds. Then, we divide this by the total area, which in this case is 10 acres.
When we perform the calculation: 96 pounds ÷ 10 acres, the solution we get is 9.6 pounds per acre.
So, it requires 9.6 pounds of seed to plant one acre of the field. Remember, this is an average estimation. Actual seed requirement may vary depending on the type of seed and other factors such as soil and weather conditions.
Learn more about Division here:https://brainly.com/question/33969335
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