[tex]-2\sqrt{15}(-8+10\sqrt{15}[/tex]

Answer:

[tex]\sf 59 \frac{17}{20} \: in^3[/tex]

Step-by-step explanation:

Regular-size box of crackers

Dimensions:  [tex]\sf 2 \frac{1}{4} \: in \times 9 \frac{1}{2}\:in \times 14\: in[/tex]

Snack-size box of crackers

Volume = [tex]\sf \frac{1}{5}[/tex] of the volume of a regular-size box

To calculate the volume of the snack-size box of crackers, calculate the volume of the regular-size box then multiply it by [tex]\sf \frac{1}{5}[/tex].

[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \textsf{width x length x height}\\\\\implies \textsf{Volume of regular-size box} & = \sf 9 \frac{1}{2} \times 14 \times 2 \frac{1}{4}\\\\& = \sf \dfrac{19}{2} \times 14 \times \dfrac{9}{4}\\\\& = \sf \dfrac{19 \times 14 \times 9}{2 \times 4}\\\\& = \sf \dfrac{1197}{4}\: in^3\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Volume of snack-size box} & = \sf \dfrac{1}{5} \times \textsf{volume of regular-size box}\\\\& = \sf \dfrac{1}{5} \times \dfrac{1197}{4}\\\\& = \sf \dfrac{1 \times 1197}{5 \times 4}\\\\& = \sf \dfrac{1197}{20}\\\\& = \sf 59 \dfrac{17}{20}\: in^3\end{aligned}[/tex]

Therefore, the volume of the snack-size box is [tex]\sf 59 \frac{17}{20} \: in^3[/tex]

Answer:

28 students

Step-by-step explanation:

7 times 4 = 28

there are are seven students in 4 teams, so that means there are 4 groups of seven, and you multiply them together to get how many students in the class

Answer:

28

Keyword(s):

divided, four, 7, per team, how many

Step-by-step explanation:

7 × 4 = 28

The degree measure of angle COA = 128 degree.

It is defined by the property that the sum of the interior angles of a triangle is equal to 180 degrees.

To determine the value of angle COA ,

we have to draw a line connecting CA ,

as OC and OA are the radius of the circle and therefore the sides of the triangle formed will be equal and also the angle made by them ,

angle OAC = angle OCA

Therefore angle DCA = angle DAC

By angle sum property

2x + 52 = 180

2x = 128

x = 64 degree

angle DCO = 90 degree

Therefore angle ACO = 90-64 = 26 degree

Similarly, angle CAO = 26 degree

By angle sum property

26+26+x = 180

52+x = 180

x = 128 degree

The degree measure of angle COA = 128 degree.

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Answer:

BC ≈ 11.8 m

Step-by-step explanation:

using the tangent ratio in the right triangle

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{x}{BC}[/tex] , that is

tan32° = [tex]\frac{7.4}{BC}[/tex] ( multiply both sides by BC )

BC × tan32° = 7.4 ( divide both sides by tan32° )

BC = [tex]\frac{7.4}{tan32}[/tex] ≈ 11.8 m ( to 3 sf )

Answer: $7448

Step-by-step explanation:

Year 1: 1.218x

Year 2: 1.218(1.218x)

Year 3: 1.218(1.218(1.218x))

Year 4: 1.218(1.218(1.218(1.218x)))

Year 5: 1.218(1.218(1.218(1.218(1.218x))))

Year 6: 1.218(1.218(1.218(1.218(1.218(1.218x)))))

Year 7: 1.218(1.218(1.218(1.218(1.218(1.218(1.218x))))))

Year 8: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x)))))))

Year 9: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x))))))))

Year 10: 1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218(1.218x)))))))))

Year 11: x(1.218¹¹)

Year 12: x(1.218¹²) = 79,400

x(10.6602517) = 79,400

x = 79,400/10.6602517

x=7448.22939

x = $7448

Hope this helps!

Step-by-step explanation:

v = Victor's age

m = Maria's age

v = 3m

v - 10 = 7(m - 10)

3m - 10 = 7m - 70

60 = 4m

m = 15

v = 3m = 3×15 = 45

Victor is 45 years old. Maria is 15 years old.

Answer:

y = 260

Step-by-step explanation:

locate x = 7 on the x- axis, go vertically up to meet the graph at (7, 260 )

when input is 7 then output y = 260

Answer:

h = -5

Step-by-step explanation:

1) Subtract 7th from both sides

6h = 7h + 5

6h - 7h= 7h + 5 - 7h

2) Simplify

- Combine like terms

6h - 7h = 7h + 5 - 7h

-h = 7h + 5 - 7h

- Combine like terms

-h = 7h + 5 - 7h

-h = 5

3) Divide both sides by the same factor

-h = 5

-h/-1 = 5/-1

4) Simplify

Cancel terms that are in both the numerator and denominator

h/-1 = 5/-1

h = 5/-1

Divide the numbers

h = 5/-1

h = -5

Answer:

The answer is H=-5

Step-by-step explanation:

Multiplication is the process of multiplying. Jay lost 30 pounds in a period of 6 months.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

A.) The newly recorded temperature in January will be six times the temperature in February, therefore, we can write,

January = 6 × February = 6×(-3°F) = -18°F

Hence, the newly recorded temperature in January will be equal to -18°F.

B.) Change in water level on each day of the drought was equal to -4 inches, while the drought lasted for 1 week(7days), Thus, the net change in water level can be written as,

net change = 7 × -4 = -28inches

Hence, the net change in the water level during the drought was equal to -28 inches.

C.) Jay went on a diet for six months and lost 5 pounds each month, therefore, the net change in the weight will be equal to,

Net Change = 6 × 5 = 30 pounds

Hence, Jay lost 30 pounds in a period of 6 months.

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The property identity of multiplication is applied in the given statement.

The properties of multiplication are:

From the property identity, you know that the product between any number by the number 1 equals that number. Example: 3 • 1=3.

The question shows 10=10•1. Like, it was shown previously, this occurs due to the identity property of multiplication.

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Answer:

302 degrees

Step-by-step explanation:

The population of the town in 1960 is 48.80 thousands

The equation of the model is given as:

f(t) = 42e^(0.015t)

1960 is 10 years after 1950.

This means that:

t = 10

Substitute t = 10 in f(t) = 42e^(0.015t)

f(10) = 42e^(0.015 * 10)

Evaluate

f(10) = 48.80

Hence, the population of the town in 1960 is 48.80 thousands

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Answer:

the first one

Step-by-step explanation:

the formul is y=mx+b

m is slope which is -3/2

b is y intercept and it is -3

and the addition sign will change based on if the y intercept is negative or not

Hope this helps

The probability of all heads, all tails, exactly two tails, exactly one head will be 1/8, 1/8, 3/8, and 3/8 respectively.

The complete question is given below.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

Then the total number of the event will be

Total event = 2³

Total event = 8 {HHH, HHT, HTH, THH, HTT, THT, HHT, TTT}

Then the probability of all heads will be

⇒ 1/8

Then the probability of all tails will be

⇒ 1/8

Then the probability of exactly two tails will be

⇒ 3/8

Then the probability of exactly one head will be

⇒ 3/8

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Answer:

  7

Step-by-step explanation:

We want to find the number 4-digit of positive integers n such that removing the thousands digit divides the number by 9.

__

Let the thousands digit be 'd'. Then we want to find the integer solutions to ...

  n -1000d = n/9

  n -n/9 = 1000d . . . . . . add 1000d -n/9

  8n = 9000d . . . . . . . . multiply by 9

  n = 1125d . . . . . . . . . divide by 8

The values of d that will give a suitable 4-digit value of n are 1 through 7.

When d=8, n is 9000. Removing the 9 gives 0, not 1000.

When d=9, n is 10125, not a 4-digit number.

There are 7 4-digit numbers such that removing the thousands digit gives 1/9 of the number.

Answer:

36 feet

Step-by-step explanation:

To find the area of a square or rectangle you multiply the width by the length.

Answer:

Step-by-step explanation:

Answer:

A. X= 13 and X= -3

Step-by-step explanation:

subtract 7 from both sides, simplify, break down the problems into 2 equations, solve equations, and boom once solve both equations you get 2 solutions.

The solutions to the equation are x = 13 and x = -3.

Therefore, the correct option is A.

Given is an expression |x-5| + 7 = 15, we need to solve for x,

To solve the equation |x - 5| + 7 = 15 for x, we'll need to isolate the absolute value expression and then solve for x.

Here's the step-by-step process:

Step 1: Subtract 7 from both sides of the equation:

|x - 5| = 15 - 7

|x - 5| = 8

Step 2: Break the equation into two cases, one with the positive value inside the absolute value and one with the negative value inside the absolute value.

Case 1: x - 5 is positive:

For this case, the equation |x - 5| = 8 becomes:

x - 5 = 8

Now, solve for x:

x = 8 + 5

x = 13

Case 2: x - 5 is negative:

For this case, the equation |x - 5| = 8 becomes:

-(x - 5) = 8

Simplify and solve for x:

-x + 5 = 8

-x = 8 - 5

-x = 3

Multiply both sides by -1 to isolate x:

x = -3

So, the solutions to the equation are x = 13 and x = -3.

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Answer:

C)    14 Units

Step-by-step explanation:

E2020

Answer:

Step-by-step explanation:

Time taken for task 1:

Distance= 750m= 0.75 km

Speed= 10 km/hr

Time taken1= S (distance)/ V (speed)= 0.75/10= 0.075 hr= 4 mins and 30 sec

Time taken for task 2:

t2=S/V= 20/85= 0.24 hr= 14 mins and 24 sec

Time taken for task 3:

t3= S/V = 5/14= 0.36 hr= 21 mins and 36 sec

Total time took:

T1 +T2+T3= 40 mins and 30 second (approximately)

Answer:

let n be the number then the sum of this number and 7 is n +7 and 3 times this sum is 3(n +7) 5 times the number less thirteen is 5n − 13

Step-by-step explanation:

Answer:

Part A: Yes

Part B: $30

Step-by-step explanation:

Some information is missing, but I did see a similar problem that shows a box shaped like a rectangular prism with length 5 in., width 4 in., and height 10 in.

Part A.

volume = length × width × height

volume = 5 in. × 4 in. × 10 in.

volume = 200 in.³

Since the volume has to be at least 180 in.³, then a volume of 200 in.³ will be ok since 200 is greater than 180.

Answer: Yes

Part B.

$0.15/in.³ × 200 in.³ = $30

Answer: $30

Answer: 35

Step-by-step explanation:

Angles in a triangle add to 180 degrees, so in triangle ABC, [tex]m\angle C=180-103-42=35^{\circ}[/tex].

Sp, by the corresponding angles theorem, x=35

Answer:

[tex]\pi[/tex]= 3.1415926...= c/d

Step-by-step explanation

Pie is infinite so there is no simple answer.

circumference divided by the diameter = pie

The statement that best describes the results is in tank 1, the rate at which water is used is higher.

Tank 1:

Tank 2:

The rate in tank 1 is higher than the rate in tank 2.

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Answer:

  3/4

Step-by-step explanation:

The relationship between time, speed, and distance can be used together with the travel time relations to find the desired ratio.

__

Let H represent the distance from Yan's location to home. Let S represent the distance to the stadium, and let w represent Yan's walking speed.

The time required for Yan to walk home is ...

  time = distance/speed = H/w

The time required for Yan to walk to the stadium is ...

  time = S/w

The time required for Yan to ride his bike from home to the stadium is ...

  time = (H +S)/(7w) . . . . . his riding speed is 7 times his walking speed.

In order for the travel times to be equal, we must have ...

  time to walk home + time to bike to stadium = time to walk to stadium

  H/w + (H +S)/(7w) = S/w

__

Multiplying by 7w gives ...

  7H +(H +S) = 7S

  8H = 6S . . . . . . . . . subtract S

  H/S = 6/8 = 3/4 . . . . divide by 8S

The ratio of Yan's distance from home to his distance from the stadium is 3/4.

_____

Additional comment

Another way to think about this is ...

The stadium is farther away than home by a distance that Yan can walk in the same time he can bike the entire distance from home to the stadium. That is, the difference in distances must be 1/7 of the total distance. Now, we have a "sum and difference" problem: S +H = 7, S -H = 1. The solution is S = (7+1)/2 = 4, H = (7-1)/2 = 3. H/S = 3/4.

Answer:

35°

Step-by-step explanation:

Same-Side interior angles (consecutive angles) are supplementary.

Supplementary meaning that those two angles add up to make 180°.

So Angles C is 35°

Answer:

The slope of the line is:  

              [tex]-\frac{3}{4}[/tex]

Slope of a parallel line is the same:

             [tex]-\frac{3}{4}[/tex]

Slope of a perpendicular line, invert the sign and fraction:

              [tex]\frac{4}{3}[/tex]

Hope this helps