Decide whether 2x + 8 and 2(x + 4) + 4 are equivalent expressions. Explain how you know.

The number of hours when the two stocks would be the same is 1.68 hours.

The first step is to determine the price of stock A at noon.

Price of stock A at noon = price at 9am + (rate of increase per hour x time difference)

Time difference = 12 - 9am = 3 hours

= $13.92 + (0.11 x 3)

= $13.92 + 0.33

= $14.25

Value of stock A t hours after noon = $14.25 + (0.11 x t)

= $14.25 + 0.11t

The equation that can be used to determine the price of stock B at time t is:

Price of stock B at time t = beginning price - (rate of decline x time)

= $14.67 - (0.14 x t)

= $14.67 - 0.14t

When the two stocks are the same, the two equations would be equal to each other:

$14.25 + 0.11t = $14.67 - 0.14t

solve for t:

0.11t + 0.14t = $14.67 - $14.25

0.25t = 0.42

t = 0.42 / 0.25

t = 1.68 hours

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Answer:

<

Step-by-step explanation:

1) Substitute 5 into the question

2) Work out the sides

3) Put it into an inequality

5 < 7

Hope this helps, have a great day!

Answer:

-0.9

Step-by-step explanation:

it is closer to 0

The total materials handling cost allocated to the modular homes is $246,372.84.

The total materials handling cost allocated to the Prefab Barns is closest to $108,000.

To allocate materials handling cost based on material moves, we must determine proportion of material moves for each product and then apply that proportion to the total materials handling cost.

Proportion of material moves for Modular Homes:

= (Total expected material moves for Modular Homes) / (Total expected material moves for both products)

= 590 / (590 + 190)

= 0.756

Total materials handling cost allocated to Modular Homes:

= Proportion of material moves for Modular Homes * Total materials handling cost

= 0.756 * $325,890

= 246 372.84

= $246,372.84.

To allocate the materials handling cost based on direct labor-hours, we need to determine proportion of direct labor-hours for each product.

For Modular Homes:

Total direct labor-hours for Modular Homes:

= 6,000 units * 800 hours/unit

= 4,800,000 hours

For Prefab Barns:

Total direct labor-hours for Prefab Barns:

= 9,000 units * 300 hours/unit

= 2,700,000 hours

Total direct labor-hours for both products:

= 4,800,000 hours + 2,700,000 hours

= 7,500,000 hours

Proportion of direct labor-hours for Prefab Barns:

= 2,700,000 hours / 7,500,000 hours

= 0.36

Allocated materials handling cost for Prefab Barns:

= Proportion of direct labor-hours for Prefab Barns * Total materials handling cost

= 0.36 * $300,000

= $108,000.

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Answer:

7/13

Step-by-step explanation:

Arrange the numbers so that the number of girls in year 10 is the numerator, and the total number of girls is the denominator. (140/260) Simplify this by dividing both numbers by 20.

Answer:

2470

Step-by-step explanation:

yeah-ya .... right?

Answer:

2,470

Step-by-step explanation:

(2*1000)+(4*100)+(7*10)

2000+400+7

2,470

Answer:

Step-by-step explanation:

Answer:

Equal to, c^2, a^2+b^2, a^2 + b^2 = c^2

Answer:

The combined area of the shaded triangles in Figure one is equal to the combined area of the shadead triangles in figure 2. The area of the unshaded square in Figure 1 can be represented by c^2. The combined area of the two unshaded squares in Figure 2 can be represented by a^2+b^2. The areas of the squares in Figure 1 and Figure 2 who that a^2+b^2=c^2.

Step-by-step explanation:

I'm right and if you think I'm wrong then you're wrong

Answer:

c

Step-by-step explanation:

it is c because it said girls to boys, then explained girls to boys, while b was out of order. a and d said 5 first, contrary to the original question

Answer:

C because all the other options are from boys to girls or 5 to 2 and were looking for girls to boys or 2 to 5.

Step-by-step explanation:

0.065

To convert a percent to a decimal, you move the decimal point to the left two times

Answer: 0.065

Step-by-step explanation:

When we divide 50 by 100 we get 0.5 (a decimal number). So, to convert from percent to decimal: divide by 100, and remove the percent symbol. So for 6.5% divided by 100=0.065

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

The scale of the drawing is 1 cm to 90 m. This means that every 1 cm on the drawing represents 90 m in real life. The length of the field is 450 m, so the length of the drawing will be 450 m / 90 m = 5 cm.

Therefore, the length of the dam drawing is 5 cm.

Step-by-step explanation:

The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Answer:

The value is  \(P(X > 500 ) = 0.011942\)

Step-by-step explanation:

From the question we are told that

       The mean is  \(\mu = 430\)

       The standard deviation is  \(\sigma = 120\)

       The sample size is  n  =  15

Generally  the probability that the sample mean is above 500

Gnerally the standard error of mean is mathematically represented as

             \(s = \frac{\sigma }{ \sqrt{n} }\)

=>          \(s = \frac{ 120 }{ \sqrt{15} }\)

=>           \(s = 30.984\)

Generally  the probability that the sample mean is above 500

     \(P(X > 500 ) = P( \frac{X - \mu }{\sigma_x} > \frac{500 - 430 }{ 30.984 } )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

       \(P(X > 500 ) = P( Z > 2.259 )\)

=>     \(P(X > 500 ) = P( Z > 2.259 )\)

From the z table  the area under the normal curve to the right  corresponding to  2.259  is

          \(P( Z > 2.259 ) = 0.011942\)

=>       \(P(X > 500 ) = 0.011942\)

Answer:

\(\boxed{\bf \angle \: C = 62^{o} }\)

Step-by-step explanation:

The sum of the opposite angle of cyclic quadrilateral is 180°.

First, lets find x...

Now, let's find the measure of angle C....

________________________

Answer: 1.04 I think

Step-by-step explanation:

Answer:

1.04

Step-by-step explanation:

26x4=104 and I put the decimal point in.

Answer:

Here is decimal form : 0.04166666666

And here is fraction form :): 1/24  Hope this helps!

Step-by-step explanation:

how to calculate 1/4 divided by 6. I will give you the answer in fraction form and in decimal form.

Here is 1/4 divided by 6 displayed mathematically in colors:

1 /4   ÷ 6

The numbers in 1/4 divided by 6 are labeled below:

1 = numerator

4 = denominator

6 = whole number

To make it a fraction form answer, you keep the numerator and multiply the denominator by the whole number to make a new denominator:

1 /4 x 6 =    

1 /24

Thus, the answer to 1/4 divided by 6 in fraction form is:

1 /24

DECIMAL FORM :)

to make the answer to 1/4 divided by 6 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

1/24 = 0.0417

The answer is rounded to the nearest four decimal points if necessary.

The best option based on the return on investment will be option 2.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

The total amount that will be paid back by Theo will be:

= Monthly installments × Number of months

= 8313 × 48

= 399302.16

The return on investment for option 1 will be:

Interest = Principal × Rate × Time

= 9000 × 0.08 × 3

= 2160

Total amount after three years will be:

= 9000 + 2160

= 11160

The return on investment for option 2 will be:

= 9000 × (1 + 0.07)³

= 11025.39

Therefore, 2 is better.

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Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

Answer:

So the breadth of the rectangle is y= 3.39 inches

And the length is = x= 4y= 4* 3.39= 13.56 inches

Step-by-step explanation:

Let the length of the rectangle be given by x and the breadth be defined by y.

Then according to the area of rectangle

Area= Length * breadth

But length is 4 times its width so x= 4y  

Therefore putting the values

Area= Length * breadth

46= x*y

46= 4y*y

46/4= y²

or

y ²= 11.5

Now taking the square root of both sides we get

y= √11.5=3.39116 inches

So the breadth of the rectangle is y= 3.39 inches

And the length is = x= 4y= 4* 3.39= 13.56 inches

-4(0.25b-2) - (7 - b) + 3/2 (4b - 2/3)

We must open the parenthesis first by multiplying the elements in it be the elements outside

Bearing in mind that

- * - = +

- * + = -

-4(0.25b-2) - (7 - b) + 3/2 (4b - 2/3)

= -b - 8 -7 + b + 6b - 1

Now we rearrange so all like terms are together noting the signs before each term

= -b + b + 6b - 8 - 7 - 1

= 6b - 16

You may leave the answer in this form or go further to factorize

= 2 (3b - 8)

Answer: step 3 maybe?

Step-by-step explanation:

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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The largest force p that can be applied to the bracket shown - P = 80 MPa × (b × h).

Largest force P that can be applied to the bracket, we need to consider the allowable stress in section ABD, which is given as 80 MPa.
Step 1: Identify the relevant variables
- Allowable stress in section ABD: 80 MPa
Step 2: Determine the cross-sectional area of section ABD
- We need the dimensions of section ABD to calculate the area.

Let's assume the width (b) and height (h) are given.
- Cross-sectional area of section ABD = b × h
Step 3: Apply the stress formula
- Stress = Force / Area
- Allowable stress in section ABD = Force P / Area of section ABD
Step 4: Solve for the largest force P
- 80 MPa = P / (b × h)
- P = 80 MPa × (b × h)

Now that we have a formula for the largest force P, you can plug in the specific dimensions of section ABD (width and height) to find the exact value of P.

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From the given information, the measure of DEF is 81°

From the question, we are to determine the measure of DEF

From the given information,

DEF and RST are complementary angles. This means they sum up to 90°

Thus,

(3(-5 + 2x)) + (x - 7) = 90

(3(-5 + 2x)) + (x - 7) = 90

(-15 + 6x) + (x - 7 ) = 90

-15 + 6x + x - 7 = 90

6x + x = 90 + 15 + 7

7x = 112

x = 112/7

x = 16

Then, substitute the value of x to determine the measure of DEF

(3(-5 + 2x))

= (3(-5 + 2(16)))

= (3(-5 + 32))

= (3(27))

= 81°

Hence, the measure of DEF is 81°

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Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35

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Answer:

y=3x2-24x+58

Step-by-step explanation:

just took the quiz