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Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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Answer: 5 hours

Step-by-step explanation: 380/76

The bus will take 5 hours to reach Montreal from New York.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Distance between Montreal to New York = 380 miles

Speed of bus = 76 miles per hour

76 miles ⇒ 1 hour

1 mile ⇒ 1/76  hour

Multiply by 380 on both sides

380 miles ⇒ 380/76 hours = 5 hours.

Hence "The bus will take 5 hours to reach Montreal from New York".

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Answer:

43.6 has 3 significant figures.

Answer:

Step-by-step explanation

Correct option is A)

C.I. for the third year = Rs. 1,452.

C.I. for the second year = Rs. 1,320

∴ S.I on Rs. 1,320 for one year = Rs. 1,452− Rs. 1,320= Rs. 132.

Rate of interest =

1,320

132×100

​

=10%.

Let the original money be Rs. P.

Amount after 2 year − amount after one year =C.I. for second year.

P(1+

100

10

​

)

2

−P(1+

100

10

​

)=1,320

P[(

100

110

​

)

2

−

100

110

​

]=1,320

⇒P[(

10

11

​

)

2

−

10

11

​

]=1,320⇒P(

100

121

​

−

10

11

​

)= Rs. 1,320

⇒P×

100

11

​

=Rs.1,320⇒P=

11

1,320×100

​

= Rs. 12,000

∴ Rate of interest =10%

and Original sum of money = Rs. 12,000

Answer:it’s B

Step-by-step explanation:

The y-intercept is -6

It opens down.

1st statement is always true.

2nd statement is never true.

3rd statement is always true.

4th statement is always true.

5th statement is sometimes true.

What is dilation geometry?

Dilation is a transformation that allows you to resize an object. Dilation is a technique for making objects larger or smaller. This transformation yields an image that is identical to the original shape. However, there is a size difference in the shape. A dilation should stretch or contract the original shape.

1. The angles of dilated figures are congruent to the original figure.

  This statement is always true.

2. The sides of dilated figures are congruent.

    This statement is never true.

3. The sides of dilated figures are proportional.

    This statement is always true.

4. A rigid transformation results in congruent figures.

   This statement is always true.

5. A rigid transformation results in similar figures.

   This statement is sometimes true.

Hence,

1st statement is always true.

2nd statement is never true.

3rd statement is always true.

4th statement is always true.

5th statement is sometimes true.

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Answer:

3.75 cubic centimeters

Step-by-step explanation:

1.5*2.5*1 cubic centimeters

Answer:

3/20

Step-by-step explanation:

1/2 x 3/5 x 1/2

L x W x H is the formula

Length x Width x Height

count the squares, they're each 1/2 so multiply the number of squares with 1/2.

For example, the rectangular prism is 3 squares high, which means it's 3/6, and that simplifies to 1/2. Now you have your height. You do the same for the width and length.

Hope this helps <3

Answer:

\(0.33\)

Step-by-step explanation:

There are 6 sides on dice, therefore the sample space would be 6 (the sample space is the denominator). We were asked to find the probability of getting a 1 or a 6. Since we were given 2 options 1 or 6, it therefore means that we are trying to find the probability of the dice rolling on 2 out of the 6 sides it has. Therefore the probability would be:

\( \frac{2}{6} \: or \: \frac{1}{3} \)

A third as a decimal is

\(0.33\)

Answer:

74 Degrees

Step-by-step explanation:

How i got it was we already know a triangle equal 180 degrees so you have to just add 69 degrees by 37 degrees and once you get the answer to the subtract it by 180 degrees and you get 74 degrees.

Answer:

Option 4

Step-by-step explanation:

\(x^2+10x=-81 \\ \\ x^2+10x+25=-56 \\ \\ (x+5)^2=-56 \\ \\ x+5= \pm \sqrt{-56}=\pm 2i \sqrt{14} \\ \\ x=-5 \pm 2i \sqrt{14}\)

Answer:

To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.

Answer:

Step-by-step explanation:

100x³²

..................

Answer:

32 and 37

Step-by-step explanation:

Because the difference between the values is 5.

Answer:

\(2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25\)

Using proportions, we can say that 42 models of 100 are needed to model 4200.

Ratio and fractions are the main bases on which proportion is explained. A fraction is written as a/b, while a ratio is represented as a:b, and a proportion states that two ratios are equal. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics.

In the question, we are asked for the number of models of 100 we need to model 4200.

The given problem can be shown as a proportion with the ratio of the number of models of 100, to the model.

We know that 1 model of 100 makes a model 100.

We assume that n models of 100 makes a model 4200.

By proportion, we can show that:

n/4200 = 1/100,

or, n = 4200/100,

or, n = 42.

Thus, using proportions, we can say that 42 models of 100 are needed to model 4200.

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Answer:

There is no triangle.

Step-by-step explanation:

Answer:

Your final answer is √32 miles.

Step-by-step explanation:

Answer:

Step-by-step explanation:

area of rectangle = 8×5 = 40 cm²

area of semicircle = ½×π4² = 8π cm²

total area = 40 + 8π ≅ 65.1 cm²

:::::

area of circle = π2² = 4π in²

area of square = 4⁴ = 16 in²

blue area = 16 - 4π ≅ 3.4 in²

Answer: C: 12-7x

Step-by-step explanation:

This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.

Any difference of two squares \(a^2-b^2\) can be factored into the sum of their square roots times the difference of their square roots \((a+b)(a-b)\).

Let's factor our expression.

\(144-49x^2=(12+7x)(12-7x)\)

Out of all the options given, only \(12-7x\) is a factor. Hence, option C is correct.

Answer:

796871

Step-by-step explanation:

Based on the given conditions, formulate:

5000 x (1 - (1 + 10%) 10)

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

           1 - (1 + 10%)                                                                          

Evaluate the equation/expression:

796871.23005

Find the closest integer to

798871.23005

=  796871

The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.

In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.

Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.

However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.

Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.

This process allows us to determine the range of values for x that satisfy the inequality.

Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The statement which proves ABCD is a parallelogram is :

Answer:

Inequalities:

\(\begin{array}{|l|c|c|}\cline{1-3} \vphantom{\dfrac12} & \sf Viable & \sf Nonviable\\\cline{1-3} \vphantom{\dfrac12} (10,25)& \checkmark & \\\cline{1-3} \vphantom{\dfrac12} (10,20)&&\checkmark \\\cline{1-3} \vphantom{\dfrac12} (20,12)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (35,0)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (20,20)&&\checkmark \\\cline{1-3}\end{array}\)

Step-by-step explanation:

Definition of variables:

Given information:

The inequality that represents Barrett working no more than 35 hours is:

The inequality that represents Barrett earning at least $400 is:

To determine if each point is a viable or nonviable solution, substitute each point into the two inequalities.  If both inequalities are true, the solution is viable.

\(\begin{aligned}(10,25) \implies 10+25 &\leq 35\\35& \leq 35 \leftarrow \sf true\\\\ \implies 15(10)+10(25)&\geq400\\400&\geq 400 \leftarrow \sf true\end{aligned}\)

Therefore, point (10, 25) is a viable solution.

\(\begin{aligned}(10,20) \implies 10+20 &\leq 35\\30& \leq 35 \leftarrow \sf true\\\\ \implies 15(10)+10(20)&\geq400\\350&\geq 400 \leftarrow \sf false\end{aligned}\)

Therefore, point (10, 20) is not a viable solution.

\(\begin{aligned}(20,12) \implies 20+12 &\leq 35\\32& \leq 35 \leftarrow \sf true\\\\ \implies 15(20)+10(12)&\geq400\\420&\geq 400 \leftarrow \sf true\end{aligned}\)

Therefore, point (20, 12) is a viable solution.

\(\begin{aligned}(35,0) \implies 35+0 &\leq 35\\32& \leq 35 \leftarrow \sf true\\\\ \implies 15(35)+10(0)&\geq400\\525&\geq 400 \leftarrow \sf true\end{aligned}\)

Therefore, point (35,0) is a viable solution.

\(\begin{aligned}(20,20) \implies 20+20 &\leq 35\\40& \leq 35 \leftarrow \sf false\\\\ \implies 15(20)+10(20)&\geq400\\500&\geq 400 \leftarrow \sf true\end{aligned}\)

Therefore, point (20, 20) is not a viable solution.

\(\begin{array}{|l|c|c|}\cline{1-3} \vphantom{\dfrac12} & \sf Viable & \sf Nonviable\\\cline{1-3} \vphantom{\dfrac12} (10,25)& \checkmark & \\\cline{1-3} \vphantom{\dfrac12} (10,20)&&\checkmark \\\cline{1-3} \vphantom{\dfrac12} (20,12)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (35,0)&\checkmark& \\\cline{1-3} \vphantom{\dfrac12} (20,20)&&\checkmark \\\cline{1-3}\end{array}\)

Answer:

let x = number of cheap cards

y = number of expensive cards

x + y = 24 ( equation 1 )

(1)(x) + (3)(y) = 50

x + 3y = 50 ( equation 2 )

equation 2 - equation 1

(x + 3y) - ( x + y ) = 50 - 24

x + 3y - x -y = 26

2y = 26

y = 26/2

y = 13 expensive cards

x + y = 24

x + 13 = 24

x = 24 -13

x = 11 cheap cards

verification :

x + 3y = 50

11 + 3(13) = 50

11 + 39 = 50

50 = 50

correct.

11 cheap cards

13 expensive cards

Answer:

the action of inflating something or the condition of being inflated.

"the inflation of a balloon"

ASTRONOMY

(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.

2.

ECONOMICS

a general increase in prices and fall in the purchasing value of money.

"policies aimed at controlling inflation"

The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:

a = (279/10) cm x (178/10) cm

Simplifying this expression, we get:

a = 4953/100 cm^2

So, the correct equations are:

B) 178/10 x 279/10 = a

and

D) a ÷ 178/10 = 279/10