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3 years ago

Simplify using the distributive property: 2a + 4(a+5) - 7

Mathematics

2 answers:

12345 [234]3 years ago

5 0

Answer: 6a + 13

Step-by-step explanation: here you go: 2a + 4*(a+5) - 7

first we simplify the brackets (distributive property, you multiply 4 "a" times plus 5 times): 2a + 4a + 20 - 7

then you add those that multiply the variable separately from those that don't: 6a + 13

likoan [24]3 years ago

4 0

Answer:

6a + 13

Step-by-step explanation:

Given

2a + 4(a + 5) - 7 ← distribute parenthesis

= 2a + 4a + 20 - 7 ← collect like terms

= 6a + 13

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Human body temperatures have a mean of 98.20° F and a standard deviation of 0.62° F. Sally's temperature can be described by z =

irina1246 [14]

Answer:

Sally's temperature is 97.27 °F.

Step-by-step explanation:

All the information given in the question tells us that the human body temperatures are normally distributed with a population's mean = 98.20°F and a standard deviation = 0.62°F.

The question gives us Sally's temperature in a z-score. We have to remember that the standard normal distribution is a particular case of a normal distribution where the mean = 0 and the standard deviation = 1.

Using the standard normal distribution, we can determine every probability associated with a normal distribution "transforming" the raw scores, coming from normally distributed data, into z-scores.

A z-score gives us the distance from the population's mean and is in standard deviation units. So, a z = 1.5 tells us that the value is 1.5 standard deviations above the mean. Conversely, a z = -1.5 tells us that the raw score is also 1.5 standard deviation from the mean, but in the opposite direction, that is, below the mean.

The formula for a z-score is as follows:

$\\ z = \frac{x - \mu}{\sigma}$ (1)

Where

$\\ x\;is\;the\;raw\;score$ .

$\\ \mu\;is\;the\;population\;mean$ .

$\\ \sigma\;is\;the\;population\;standard\;deviation$ .

Then to find x (or the raw score, that is, Sally's temperature), we need to solve the formula (1) for it to finally solve the question.

Then

$\\ \mu = 98.20^\circF$ °F

$\\ \sigma = 0.62^\circF$ °F

$\\ z = -1.5$

Thus (with no units)

$\\ -1.5 = \frac{x - 98.20}{0.62}$

$\\ (-1.5*0.62) = x - 98.20$

$\\ (-1.5*0.62) + 98.20 = x$

$\\ x = (-1.5*0.62) + 98.20$

$\\ -0.93 + 98.20$

$\\ x = 97.27$ °F

Thus, Sally's temperature is $\\ x = 97.27$ °F (rounding the answer to the nearest hundredth).

8 0

3 years ago

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Juan wants to make a new game board that is a grid containing 25 equally sized squares. How many squares should be shaded to cre

pickupchik [31]

Let the number of shaded square be x. And it is given that total number of squares are 25.

$probability = \frac{shaded \ squares}{total \ squares}$

Substituting the values

$0.2 = \frac{x}{25}$

Performing cross multiplication

$0.2*25=x \\ x = 5$

So 5 squares should be shaded to create a region with a geometric probability of 0.2 .

8 0

3 years ago

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We have two stacks of styrofoam cups. One stack has 6 cups, and its height is 15 cm. The other stack has 12 cups, and its height

Irina18 [472]

Complete Question

We have two stacks of styrofoam cups. One stack has 6 cups, and its height is 15 cm. The other stack has 12 cups, and its height is 23 cm. How many cups are needed for a stack with a height of 50 cm

Answer:

37.5 cups

Step-by-step explanation:

Height 1 = 15cm

Number of cups = 6

Height 2 = 23 cm

Number of cups = 12

Hence:

H1 - H2/N1 - N2

= 15 - 23/6 - 12

= -8/-6

= 4/3

The number of cups that are needed for a stack with a height of 50 cm is calculated as:

50 cm ÷ 4/3

= 50 × 3/4

= 37.5 cups

3 0

2 years ago

If x + 3 is a factor of x3+3x2+ax−12, what is the value of a?

marissa [1.9K]

Answer: -4

Step-by-step explanation:

p(x)=x^3+3x^2+ax-12

x+3 is factors means it divide completely so x=-3

p(-3)=(-3)^3+3(-3)^2+a(-3)-12

-27+27-3a-12=0

-3a-12=0

3a=-12

a=-12/3

a=-4

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2 years ago

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The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scal

Art [367]

Answer:

Step-by-step explanation:

12 / 2 = 6

5 / 2 = 2.5

6 x 2.5 = 15

15 inches²

8 0

2 years ago