Question 4 of 10
One spring, a group of students measured rainfall totals at their school. This
chart shows how many inches of rain the students measured each month.
How much total rainfall did they receive at their school that spring?
MONTH
March
April
May
Subtracting Decimals in Word Problems
RAINFALL
1.1
4.1
6.1

Answer:yo it’s me leo remember me my acount got deleted

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

12+3=5x-3+3

15=5x

15=5(3)

15=15

The equation that can be used to find the solution is -d + 5 = 4

Given the indices expression below;

\((\frac{1}{3} )^{d-5}=81\)

Rewrite to base of 3 to have:

\((3^{-1})^{d-5}= 3^4\\3^{-d+5}= 3^4\)

Cancel the base and equate the power

-d + 5 = 4

Hence the equation that can be used to find the solution is -d + 5 = 4

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Answer:

x<−19

Step-by-step explanation:

First add 9 to both sides since you want to get x by itself.

-9 +9 x < -28+9

Finally, you have your answer.

x<-19

Answer:

Answer:

Move all terms not containing  

x

to the right side of the inequality.

Inequality Form:

x<-9

Interval Notation:

(-∞,-19)

Step-by-step explanation:

Answer: p = 1

Step-by-step explanation:

2/5 + p = 4/5 + 3/5p

-2/5        -2/5

      p = 2/5 + 3/5p

-3/5p            -3/5p

2/5p = 2/5

Divide both sides by 2/5

p = 1

Answer:

10

Step-by-step explanation:

Using an exponential function, it is found that the hourly growth rate of the bacteria culture is of 14.9%.

------------------------

An exponential function has the following format:

\(A(t) = A(0)(1+r)^t\)

In which:

------------------------

Since it doubles every 5 hours, it means that:

\(A(5) = 2A(0)\)

And we use this to find r.

------------------------

\(A(t) = A(0)(1+r)^t\)

\(2A(0) = A(0)(1+r)^5\)

\((1 + r)^5 = 2\)

\(\sqrt[5]{(1 + r)^5} = \sqrt[5]{2}\)

\(1 + r = 2^{\frac{1}{5}}\)

\(1 + r = 1.149\)

\(r = 1.149 - 1 = 0.149\)

0.149*100% = 14.9%.

The hourly growth rate of the bacteria culture is of 14.9%.

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Answer:

x is greater than or equal to 16.

Step-by-step explanation:

Hi! It says atleast 80 points, so your sign should be flipped over to show that x+64 needs to be ATLEAST 80. Then they asked you to solve for x. To solve for x, you subtract 64 from each side to get x is greater than or equal to 80-64, otherwise known as 16.

The inequality is \(x +64 \ge 80\)

It solves to \(x \ge 16\)

She needs at least 16 more points.

=========================================================

Further Explanation:

"At least 80" means "80 or more"

In other words, the lowest grade she can get is 80

x = number of points she needs

x+64 = number of points she has, after adding on the earlier 64 points

The x+64 must be 80 or larger. So the inequality to set up is \(x+64 \ge 80\)

You had the right idea, but need to flip the inequality sign.

To solve this inequality, you subtract 64 from both sides and you should end up with \(x \ge 16\)

This says she needs at least more 16 points to go with the 64 points she already has.

If we assume that each student's heart creates the same amount of energy as a single person, the energy created would be enough to drive the truck for 192000 meters.

If we assume that each student's heart creates the same amount of energy as a single person, we can estimate the total amount of energy created by the class.

If one person's heart creates enough energy to drive a truck for 32 kilometers,

Then six people's hearts would create enough energy to drive the truck for 32 x 6 = 192 kilometers.

In meters, it would be 192 x 1000 = 192000 meters.

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Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy that is created by all the students in your math class for a week, how many meters could the truck drive?

Number of students is 6

Hi there!

6 1/2 miles.

If Ian rode his scooter 2 1/6 in 1/3 of a hour x3 the number to find how many mile he traveled in a hour..

1.Multiplty 2 1/6 by x3:

\(2\frac{1}{6}\)·\(3=6\frac{3}{6}\)

2.Simplifly the fraction term:

\(6\frac{3}{6}=6\frac{1}{2}\)

Therefore, Ian traveled 6 1/2 mile in a hour.

The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV is the future value of the annuity,

P is the yearly payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.

Let's substitute these values into the formula and calculate the total value of the annuity:

FV = 693 * ((1 + 0.053)^16 - 1) / 0.053

FV = 693 * (1.053^16 - 1) / 0.053

Using a calculator, we can evaluate the expression inside the parentheses:

1.053^16 ≈ 1.9738

Substituting this value back into the formula:

FV = 693 * (1.9738 - 1) / 0.053

FV = 693 * 0.9738 / 0.053

FV ≈ 12739.62

Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

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Answer:

87, 73 (solution A)

Step-by-step explanation:

We know that angle WXY is 160 degrees. Therefore, (5x+8)+(7x-4)=160.

(5x+8)+(7x-4)=160

5x+8+7x-4=160

12x=156

x=13

Now that we have x, we can plug them in to the expressions to find the measures of the given angles.

7(13)-4=87 degrees (angle WXZ)

5(13)+8=73 degrees (angle YXZ)

Answer:

19

Step-by-step explanation:

9+10 is not 21 it is 19.

If 2 tens make a 20 and 1 number is gone, 20-1=19

Answer:

Step 1: Place the compass needle on vertex A, adjust the width of the compass to a medium setting, and draw one arc on line segment AB and one on line segment AC.

Step 2: Place the compass needle on the point where the arc intersects line segment AB and draw an arc inside the triangle. Without changing the compass setting, place the compass needle on the point where the arc intersects line segment AC; draw another arc intersecting the arc already inside the triangle. Label the point of intersection P.

Step 3: Draw line segment AP. This is the angle bisector of angle A.

Step 4: Place the compass needle on vertex C, adjust its width to a medium setting, and draw arcs intersecting line segment BC and line segment AC.

Step 5: Place the compass needle on the point where the arc intersects line segment BC, and draw an arc inside the triangle. Without changing its setting, place the compass on the point where the arc intersects line segment AC; draw another arc intersecting the arc already inside the triangle. Label the point of intersection Q.

Step 6: Draw line segment CQ. This is the angle bisector of angle C.

Step 7: Label the intersection of the angle bisectors M. This is the center of the inscribed circle.

Step 8: Place the compass needle on M, and draw two arcs on line segment BC.

Step 9: Place the compass needle on one of the points where an arc intersects line segment BC, and draw an arc outside the triangle; repeat from the point where the other arc intersects line segment BC to create two intersecting arcs outside the triangle. Draw a line from M passing through the point of intersection outside the triangle. This is a perpendicular line from M to line segment BC. Mark the point where the line intersects line segment BC, and label it N.

Step 10: Place the compass needle on M, set its width to N, and draw a circle. This is the inscribed circle of triangle ABC.

Answer: 1/6

Step-by-step explanation: It was the first question on my quiz, hope it helped:)

The equivalent value of the expression \(36^{-(\frac{1}{2})\) is, 1/6.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An expression \(36^{-(\frac{1}{2})\).

We know, 6×6 = 36 = 6².

Therefore, \(36^{-(\frac{1}{2})} = (6^2)^{-(\frac{1}{2})\).

\((6^2)^{-(\frac{1}{2})} = (6)^{2\times{-(\frac{1}{2})\).

= 6⁻¹.

= 1/6.

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Answer:

Never, unless they already have some points to even the points out

Step-by-step explanation:

Answer:

15 dollars

Step-by-step explanation:

Total Bill = Cost of the Meal + tip

Total Bill = 100 + 15/100 * 100

Total Bill = 115

So the tip is 15 dollars.

Given :

Point A and point B are placed on a number line.

Point A is located at -5 and point B is 10 less than point A.

To Find :

Position of point B in number line.

Solution :

It is given that position of point A is -5 on number line.

So, value of A is -5.

Now, it is given that point B is 10 less than point A.

B = [ -5 + ( -10 ) ] =  -15

Therefore, position of point B is [ -5 + ( -10 ) ] = -15 .

Answer:

3, 6, and 8 for a triangle

Step-by-step explanation:

So, let's start with what we know

The sum of the 2 lesser lengths of a triangle must be greater than the greatest length of a triangle. Otherwise, it cannot be a triangle

a + b > c

Note: variables a and b are the lesser lengths of a triangle, and c is the greatest length.

We are to list out the possible combinations of triangles here with lengths  1, 3, 6, and 8.

So, with the formula above, we will get the combination of

3,6,8

Any other combinations of triangle lengths will not work

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Answer:

distance between home and office = 3 km

Step-by-step explanation:

Answer:

9.18%

Step-by-step explanation:

The probability of getting a tail on a fair coin flip is 0.5, and the probability of getting a head is also 0.5. Since each coin flip is independent, we can use the binomial probability formula to calculate the probability of getting exactly 5 tails in 15 flips:

P(X = 5) = (15 choose 5) * (0.5)^5 * (0.5)^(15-5)

where (15 choose 5) is the number of ways to choose 5 tails out of 15 flips, which can be calculated as:

(15 choose 5) = 15! / (5! * 10!) = 3003

Substituting the values, we get:

P(X = 5) = 3003 * (0.5)^15 ≈ 0.0918

Therefore, the probability of getting exactly 5 tails in 15 coin flips is approximately 0.0918 or 9.18%.

Answer:

Perimeter:44.91

Area:123.5

Step-by-step explanation:

Perimeter: Starting with the semi circle, the circle has a radius of 5, and pi*radius^2 = 2*pi*radius=pi*5*2=3.14*10 = 31.4

that is the circumference for a whole circle, so the semi circle is 31.4/2=15.7

the perimeter of the triangle is 7+10+ sqrt(7^2+10^2)= sqrt(49+100) = sqrt(149)=12.21

12.21+7+10+15.7=44.91

area: area of the triangle is 7*10=70 70/2 = 45

area of the semicircle is 5 squared * 3.14 which is 25*3.14 which is 78.5

45+78.5= 123.5

The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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Answer:

(i) Triangle ABC and triangle ADE are similar triangles. Hence, their ratios will be same.

Ratio of DE to BC is 4:6 => 2:3

To find area, we need to raise the ratio of length to power 2

(2/3)² = 16/x

4/9 = 16/x

x = (16*9)/4

x = 36cm²

Therefore, area of triangle ABC is 36cm²

(ii) Ratio of DE to BC is 4:8 => 1:2

(1/2)² = 25/x

1/4 = 25/x

x = 25*4

x = 100cm²

Therefore, area of triangle ABC is 100cm²

I'm not sure about the third question, sorry

Step-by-step explanation:

The volumes of the prisms are :- 1) 11760 units³, 2) 7938 units³, 3) 9261 units³, 4) 22800 unit³, 5) 11781 units³, 6) 38936 units³, 7) 23125 units³, 8) 26208 units³ and 9) 14688 units³

A prism is a solid shape that is bound on all its sides by plane faces.

Given are prisms, we need to find their volumes :-

Volume = area of base × height

1) Base is a rectangle, area = length × width, height = 24

Volume = 24·14·35 = 11760 units³

2) Base is a rectangle, area = length × width, height = 21

Volume = 21·14·27 = 7938 units³

3) This is a cube, with side 21 units

Volume of cube = side³ = 9261 units³

4) This is a trapezoidal prism,

Volume = 1/2(b1+b2) × height × length = 1/2(36+24) × 38 × 20

= 22800 unit³

5) This is a triangular prism,

Volume = 1/2 × height × length × base

= 1/2 × 33 × 34 × 21 = 11781 units³

6) This is a cylinder,

Base is circular, volume = π·radius²·height

= 3.14·20·20·31 = 38936 units³

7) Base is a rectangle, area = length × width, height = 37

Volume = 25·37·25 = 23125 units³

8) Base is a rectangle, area = length × width, height = 28

Volume = 39·24·28 = 26208 units³

9) Base is a rectangle, area = length × width, height = 36

Volume = 36·24·17 = 14688 units³

Hence, the volumes of the prisms are :- 1) 11760 units³, 2) 7938 units³, 3) 9261 units³, 4) 22800 unit³, 5) 11781 units³, 6) 38936 units³, 7) 23125 units³, 8) 26208 units³ and 9) 14688 units³

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The volume in cubic inches of the prism is 528 cubic inches.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of the Cuboid.

The volume is calculated as:-

V = L  x  W  x  H

V = 6  x  11  x   8  

V = 528 cubic inches

Therefore the volume in cubic inches of the prism is 528 cubic inches.

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Answer:

Step-by-step explanation:

The domain and range of a linear function is always real numbers (T or F)

It is True. This is because of a couple of reasons.

    1.) You cannot divide by 0.

     2. A negative number cannot have its square root taken.

The range is determined by the domain in a linear function, and thus it must always consist of real numbers.

Answer:

×=14

Step-by-step explanation:

24÷16=1.5

21÷1.5=14

Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6

Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units