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Delicious77 [7]

2 years ago

8

Jackie has fewer than 20 h to work on her jewelry. It takes her half an hour to make a necklace and an hour to make a bracelet.

She wants to make x necklaces and y bracelets, and she wants at least twice as many bracelets as necklaces.
Select all inequalities that model this situation.

y>2x

x>0

0.5x+y≤20

0.5x+y<20

x≥0

y≥2x

Adam needs both small and large cones to set up for a soccer practice. He knows there are fewer than 30 cones in the storage room. He needs at least a dozen large cones.

Let x represent the number of small cones and y represent the number of large cones.

Select all inequalities that model this situation.

y≥12

x+y≤30

x>0

y>12

x+y<30

x≥0

1 answer:

aivan3 [116]2 years ago

8 0

Question 1.

(Jackie)

0.5x+y<20

y≥2x

x≥0

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Triangle A has a height of 2.5\text{ cm}2.5 cm2, point, 5, start text, space, c, m, end text and a base of 1.6\text{ cm}1.6 cm1,

konstantin123 [22]

Answer:

Option A

Option D

Option E

Step-by-step explanation:

we know that

If the height and base of triangle B are proportional to the height and base of triangle A

then

Triangle A and Triangle B are similar

Remember that

If two triangles are similar then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

$\frac{h_A}{h_B} =\frac{b_A}{b_B}$

where

h_A and h_B are the height of triangle A and triangle B

b_A and b_B are the base of triangle A and triangle B

In his problem we have

$h_A=2.5\ cm\\b_A=1.6\ cm$

substitute

$\frac{2.5}{h_B} =\frac{1.6}{b_B}$

Rewrite

$\frac{2.5}{1.6} =\frac{h_B}{b_B}$

$\frac{h_B}{b_B}=1.5625$

<u><em>Verify all the options</em></u>

A) we have

$h_B=2.75\ cm\\b_B=1.76\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{2.75}{1.76}=1.5625$

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

B) we have

$h_B=9.25\ cm\\b_B=9.16\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{9.25}{9.16}=1.0098$

The ratios are not equal

That means that are not proportional

therefore

These values could not be the height and base of triangle B

C) we have

$h_B=3.2\ cm\\b_B=5\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{3.2}{5}=0.64$

The ratios are not the same

That means that are not proportional

therefore

These values could not be the height and base of triangle B

D) we have

$h_B=1.25\ cm\\b_B=0.8\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{1.25}{0.8}=1.5625$

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

E) we have

$h_B=2\ cm\\b_B=1.28\ cm$

Find the ratio of the height to the base of triangle B and compare the result with the ratio of height to the base of triangle A (the value is 1.5625)

substitute the values in the proportion

$\frac{2}{1.28}=1.5625$

The ratios are the same

That means that are proportional

therefore

These values could be the height and base of triangle B

8 0

2 years ago

Which pair of expressions has equivalent values? 1 Superscript 13 and 1 Superscript 15 6 Superscript 1 and 9 Superscript 1 7 Sup

lora16 [44]

Answer:

1 Superscript 13 and 1 Superscript 15

Step-by-step explanation:

The process of exponentiation can be mathematically written as:

a^b

where a is called the base, and b is called the exponent.

Basically it means that we have to multiply the base with itself as many times as the value of the exponent.

For example 2^4 is 2•2•2•2

Having this in mind, 1^13 and 1^15 have equivalent values, because no matter how many times we multiply 1 with itself it will always be equal to 1.

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2 years ago

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Solve for x in the equation x squared minus 12 x + 36 = 90. x = 6 plus-or-minus 3 StartRoot 10 EndRoot x = 6 plus-or-minus 2 Sta

goldenfox [79]

Answer: x = 6 plus-or-minus 3 StartRoot 10

Step-by-step explanation:

The given quadratic equation is expressed as

x² - 12x + 36 = 90

Rearranging the equation so that it takes the the standard form of

ax² + bx + c, it becomes

x² - 12x + 36 - 90 = 0

x² - 12x - 54 = 0

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 1

b = - 12

c = - 54

Therefore,

x = [- - 12 ± √(- 12² - 4 × 1 × - 54)]/2 × 1

x = [12 ± √(144 + 216)]/2

x = [12 ± √360]/2

x = (12 ± 6√10)/2

x = 6 + 3√10

3 0

2 years ago

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Find H.C.F. and L.C.M. of x3-y3, x2-y2 and (x-y) ?

maks197457 [2]

Answer:

1) x³-y³ = (x-y)(x²-xy+y²)

2)x²-y² =(x-y)(x+y)

3)x-y = (x-y)

hcf = (x-y)

lcm = (x-y)(x²-xy+y²)(x+y)= (x³-y³)(x+y)

Step-by-step explanation:

5 0

2 years ago

From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 265. A thermostat used in an electri

Leviafan [203]

Answer:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=201.77$ represent the sample mean

$s=2.41$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =200$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :

Null hypothesis: $\mu = 200$

Alternative hypothesis: $\mu = 200$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The statistic is given by:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

4 0

2 years ago