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Goryan [66]
3 years ago
7

A teacher is buying supplies for an upcoming art project. She buys x bottles of paint for $1.29 each. She buys 8 more canvases t

han bottles of
paint for $1.89 each. Her total pretax cost is $37.38. How many of each item is she buying?​
Mathematics
1 answer:
Alina [70]3 years ago
4 0

Answer:

She is buying 7 bottles and 15 canvases of paint

Step-by-step explanation:

* <em>Lets change the story problem to equations and solve them</em>

- The teacher buys x bottles of paint for $1.29 each

- She buys 8 more canvases than bottles of  paint for $1.89 each

- Her total pretax cost is $37.38

* <em>Lets write an equation represented these information</em>

∵ x is the number of the bottles of paint

∵ She buys 8 more canvases than bottles

∴ The number of canvases of paint = x + 8

∵ Her total pretax is $37.38

∵ The cost of a bottle of paint is $1.29

∵ The cost of a canvas of paint is $1.89

∴ 1.29(x) + 1.89(x + 8) = 37.38

- Simplify the equation

∴ 1.29 x + 1.89 x + 15.12 = 37.38

∴ 3.18 x + 15.12 = 37.38

- Subtract 15.12 from both sides

∴ 3.18 x = 22.26

- Divide both sides by 3.18

∴ x = 7

∵ x represents the number of bottles

∴ The number of bottles of paint is 7

∵ x + 8 represents the number of canvases

∴ The number of canvases = 7 + 8 = 15

∴ The number of canvases of paint is 15

∴ She is buying 7 bottles and 15 canvases of paint

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Elenna [48]

Answer:

144

Step-by-step explanation:

5 0
3 years ago
rectangle with a perimeter of 1110 meters, this rectangular shape is 30 meters longer than 6 times its width. find its dimension
Alecsey [184]

Answer:

The width of the rectangle is  75 meters and length is 480 meters.

Step-by-step explanation:

The perimeter of the rectangle = 1110 meters

Let the width of the rectangle = k meters

So,the length of the rectangle = 6k + 30

Now, PERIMETER OF A RECTANGLE = 2(LENGTH + WIDTH)

⇒ 1110 = 2( k + (6k + 30))

or, 1110 = 14 k + 60

or, 14 k = 1110 - 60 = 1050

⇒ k = 1050/14 = 75

Hence, the width of the rectangle is k =  75 meters

and the Length of the rectangle is 6k + 30 = 6(75) +30

= 480 meters

6 0
3 years ago
Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14
denis-greek [22]

Answer:

Option (c) is correct.

68% of the data points lie between 10 and 18.

Step-by-step explanation:

Given :  a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the  sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean  and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.

4 0
3 years ago
Consider a population of Pacific tree frogs (Pseudacris regilla). In this population of frogs, a single locus controls the produ
zloy xaker [14]

Answer:

Step-by-step explanation:

Hello!

Use these data to calculate the chi-square statistic. Report your calculated chi-square statistic to two decimal places.

In this example, the study variable is X: genotype of a single locus two allele gene that codes the mating call of tree frogs. Categorized: S₁S₁, S₁S₂, and S₂S₂.

Usually, when you have a sample of observed genotypes of a gene of interest, the goal is to check if these genotypes follow a theoretical model such as the frequency models proposed by Mendel.

In Mendelian genetics, when two heterozygous individuals (Aa, Aa) from the F1 generation are crossed, you expect the next generation (F2) to show the genotypic ratio 1:2:1 ⇒ This model means that out of 4 descendants 1 will have the genotype AA, 2 will have the genotype Aa and 1 will have the genotype aa. Since there is no theoretical model specified I'll use the mendelian ratio 1:2:1.

If this theory applies to the population then we'll expect that the proportion of the first genotype is P(S₁S₁)= 0.25, the second P(S₁S₂)= 0.5 and the third P(S₂S₂)=0.25

To test if the observed genotypes follow the theoretical model you have to apply a Chi-Square Goodness of Fit Test.

For this test the hypotheses are:

H₀:P(S₁S₁)= 0.25; P(S₁S₂)= 0.5; P(S₂S₂)=0.25

H₁: The data is not consistent with the specified distribution.

α: 0.05

Statistic: X^2= sum(\frac{(o_i-e_i)^2}{e_i} )~X^2_{k-1}

Where:

oi: Observed frequency for the i- category

ei: Expected frequency for the i-category

k= number of categories

The rejection region for this test is one-tailed to the right. This is so because if the observed and expected values are too different (the chi-square value will be high) this will mean that the population doesn't follow the theoretical model and thus reject the null hypothesis. If the differences between what's observed and what's expected are small, this will mean that the population follows the theoretical model (and you'll obtain a small chi-square value) and you will not reject the null hypothesis.

The critical value is:

X^2_{k-1; 1 - \alpha }= X^2_{3;0.95}= 7.815

If the statistic is at least 7.815, the decision is to reject the null hypothesis.

If the statistic is less than 7.815, the decision is to not reject the null hypothesis.

Step 1 is to obtain the expected frequencies for each category:

e_i= n*P_i

e_{S_1S_1}= n * P(S_1S_1)= 1341*0.25= 335.25

e_{S_1S_2}= n * P(S_1S_2)= 1341 * 0.5= 670.5

e_{S_2S_2}= n * P(S_2S_2)= 1341*0.25= 335.25

Note: the summatory of the expected frequencies is equal to the total of observations ∑ei= n. If you have doubts about your calculations, you can add them to check it: ∑ei= 335.25 + 670.5 + 335.25= 1341

X^2= (\frac{(987-335.25)^2}{335.25} )+(\frac{(333-670.5)^2}{670.5} )+(\frac{(21-335.25)^2}{335.25} ) = 1731.50

Decision: Reject null hypothesis.

I hope this helps!

3 0
3 years ago
A spaceship weighs 410,000 kg. what is this number, without units, in scientific notation?
Nesterboy [21]

Answer:

<h3>4.1 x 10^5</h3>

Step-by-step explanation:

10^5 = 100,000 x 4.1 = 410,000

7 0
2 years ago
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