What number should go in the space? Multiplying by 1.98 is the same as increasing by ____

∠A and ∠C are right angles. m∠p = _???_ degrees.

iogann1982 [59]

Answer

Find out the m∠p .

To prove

As in ΔDAB is a right triangle

Apply pythagorean theorem

Hypotenuse ² = Perpendicular ² + Base²

DB² = AB² + AD²

AB = 5 units

AD = 6 units

Put in the above formula

DB² = 5² + 6²

= 25 + 36

= 61

$DB = \sqrt{61}\ units$

= 7.8 units (approx)

Now in ΔDCB is a right triangle .

By using the trignometric identity .

$cosp = \frac{Base}{Hypotenuse}$

$cosp = \frac{DC}{DB}$

As DC = 4 units

DB = 7.8 units (approx)

Put all the values in the trignometric identity .

$cos p = \frac{4}{7.8}$

$\angle p = cos^{-1}(\frac{4}{7.8})$

∠p = 59.15 ° (approx)

5 0

2 years ago

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You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for

kotegsom [21]

Answer:

q(p)= -3000p+12000

Step-by-step explanation:

For the function to be linear,

q(p)= mp + c

where

q(p): number of hamburgers sold

p: price per hamburger

m: gradient of the function

c: constant of the function

q(p)=6000 when p=2

6000=2m+c .................... equation I

0=4m+c

c=-4m........................ equation II

Substitute value of c in equation I

6000=2m-4m

m= -3000

c=12000

q(p)= -3000p+12000

6 0

2 years ago

A market analyst is developing a regression model to predict monthly household expenditures on groceries as a function of family

notka56 [123]

Answer:

Monthly household expenditures on groceries

Step-by-step explanation:

The response variable is the one for which measurements are desired and that depends on other variables.

In this case, family size, household income, and household neighborhood are independent variables, while the response variable is the monthly household expenditures on groceries.

8 0

2 years ago

The functions f(x) and g(x) are described using the following equation and table: f(x) = −2(1.07)x x g(x) −4 −10 −2 −7 0 −4 2 1

Natali [406]

Answer:

The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).

Step-by-step explanation:

7 0

2 years ago

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Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately norm

natima [27]

Answer:

a) Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.

b) 69.51% of those who ran the marathon has a finishing time less than 272.

c) The spread in the distribution of women's finishing time is greater as compared to the spread in the distribution of men's finishing time.

Step-by-step explanation:

Part a) It was given that, the finishing time for Clay's marathon time is 289 minutes.

To calculate the standardized test score for Clay's marathon time, we use the formula:

$z = \frac{x - \mu}{ \sigma}$

where

$x = 289$

$\mu = 242$

and

$\sigma = 29$

We substitute the values into the formula to get:

$z = \frac{289 - 242}{29} = 1.62$

Interpretation: Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.

b) To calculate the proportion of women that had a finishing time less than Kathy , we again need to calculate the z-score for x=272, with mean for women being 259 minutes and standard deviation 32 minutes.

We substitute to get:

$z = \frac{272 - 259}{32} = 0.41$

From the standard normal distribution table, P(z<0.41)=0.6951

Therefore 69.51% of those who ran the marathon has a finishing time less than 272.

c) The standard deviation measures the variation of a distribution. This means the standard deviation measures how far away the data set of a distribution are from the mean.

If the standard deviation of finishing time is greater for women than for men, then it indicates that, women's finishing time are far away from the mean finishing time as compared to men's finishing time.

5 0

2 years ago

What number should go in the space? Multiplying by 1.98 is the same as increasing by _____%.