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the volume of a 15oz cereal box is 180.4in cube. the length of the box is 3.2 in. less than the height and the width is 2.3 in. find the height and length of the box to the nearest tenth.

Answers

Answer 1

Answer:

The height and length of the box to the nearest tenth will be 10.6 inch and 7.4 inch respectively.

Explanation

Suppose, the height of the box is $h$ inch

As the length of the box is 3.2 in. less than the height, so the length will be: $(h-3.2) inch$

Given that, the width of the box is 2.3 inch. and the volume is 180.4 inch³

Formula for Volume of a box: $V= length*width*height$

So, the equation will be....

$(h-3.2)*2.3*h = 180.4\n \n 2.3h^2 -7.36h=180.4\n \n 2.3h^2-7.36h-180.4=0$

Now using quadratic formula......

$h=(-b+/-√(b^2-4ac))/(2a)\n \n h= (-(-7.36)+/-√((-7.36)^2-4(2.3)(-180.4)))/(2(2.3))\n \n h= (7.36+/-√(1713.8496))/(4.6) \n \n h=(7.36+/-41.398...)/(4.6) \n \n h= 10.599... or -7.399...$

(Negative value of $h$ is ignored as the height can't be negative)

So, the height to the nearest tenth will be 10.6 inch and the length will be: $(10.6-3.2)inch= 7.4 inch$

Related Questions

Please help! Will Mark brainliest!
For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour. Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.
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One urn contains 8 blue balls and 12 white balls, and a second urn contains 14 blue balls and 5 white balls. An urn is selected at random, and a ball is chosen from the urn. (Round your answers to one decimal place.) (a) What is the probability (as a %) that the chosen ball is blue? (b) If the chosen ball is blue, what is the probability (as a %) that it came from the first urn? Need Help? Read It Talk to a Tutor
What is the answer to this equation?? (-3)^2=( )( )=

Use any method to multiply (-14ab)(a + 3b - 4c).

Answers

Answer:

-14a^2b-42ab^2+56abc

Step-by-step explanation:

You can use the FOIL method

multiply the first numbers

then inner

then outer

then last

$(a^(2)-1)/(2-5a) times (15a-6)/(a^(2)+5a-6)$ click on answer to see full problem

Answers

$\bf \cfrac{a^2-1}{2-5a}* \cfrac{15-6}{a^2+5a-6}\n\n-----------------------------\n\nrecall\quad \textit{difference of squares}\n \quad \n(a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\n\nthus\quad a^2-1\iff a^2-1^2\implies (a-1)(a+1)\n\n\nnow\quad a^2+5a-6\implies (a+6)(a-1)\n\n-----------------------------\n\nthus\n\n\n\cfrac{a^2-1}{2-5a}* \cfrac{15-6}{a^2+5a-6}\implies \cfrac{(a-1)(a+1)}{2-5a}* \cfrac{3(5a-2)}{(a+6)(a-1)}\n\n-----------------------------\n\n$

$\bf now\quad 3(5a-2) \iff -3(2-5a)\n\n-----------------------------\n\nthus\n\n\n\cfrac{\underline{(a-1)}(a+1)}{\underline{2-5a}}* \cfrac{-3\underline{(2-5a)}}{(a+6)\underline{(a-1)}}\implies \cfrac{-3(a+1)}{a+6}$

Brand X batteries have a mean life span of 102 hours, with a standard deviation of 6.8 hours. Brand Y batteries have a mean life span of 100 hours, with a standard deviation of 1.4 hours. Complete each of the sentences.

Answers

Answer:

Step-by-step explanation:

Hello!

X₁: Life span of a battery of Brand X

X₁~N(μ₁;σ₁²)

μ₁= 102hours

σ₁= 6.8hours

X₂: Life span of a battery of Brand Y

X₂~N(μ₂;σ²)

μ₂= 100hours

σ₂= 1.4hours

To complete the first two sentences, you have to use the empirical rule:

μ±δ= 68% of the distribution

μ±2δ= 95% of the distribution

μ±3δ= 99% of the distribution

1. About 68% of brand x’s batteries have a lifespan between 95.2 and 108.8 hours.

μ₁±σ₁= 102 ± 6.8= 95.2; 108.8

2. About 68% of brand y’s batteries have a lifespan between 98.6 and 101.4 hours.

μ₂±σ₂= 100 ± 1.4= 98.6; 101.4

3. The life span of brand Y ’s battery is more likely to be consistently close to the mean.

The standard deviations show you the dispersion of the distribution. A low standard deviation indicates that the values are close to the mean. A high standard deviation indicates that the values are further away the values are from the mean.

The standard deviation for the X batteries is σ₁= 6.8hours and the Y batteries are σ₂= 1.4hours since the standard deviation for the Y batteries is less than the standard deviation for the X batteries, you'd expect that the life span of the Y batteries will be closer to the mean than the life span of the X batteries.

I hope it helps!

Insert <, >, or = between the given pair of numbers to make a true statement.- |-11| - (-11)

Answers

Answer:

- |-11| < - (-11)

Step-by-step explanation:

Given the pair of numbers - |-11| and - (-11), we want to determine which is greater or whether they are equal

First lets rewrite both numbers.

- |-11| = -11 (note that the modulus sign will change any negative value into a positive value and that's why |-11| is equivalent to 11)

- (-11) = 11 (note that the negative sign here was retained since it is not an absolute value like the former)

It can be seen that both numbers are therefore not equal i.e - |-11| is less than - (-11). Hence the expression - |-11| < - (-11) is a true statement

A researcher wants to determine if the nicotine content of a cigarette is related to "tar". A collection of data (in milligrams) on 29 cigarettes produced the accompanying scatterplot, residuals plot, and regression analysis. Complete parts a and b below. ) Explain the meaning of Upper R squared in this context. A. The linear model on tar content accounts for 92.4% of the variability in nicotine content. B. The predicted nicotine content is equal to some constant plus 92.4% of the tar content. C. Around 92.4% of the data points have a residual with magnitude less than the constant coefficient. D. Around 92.4% of the data points fit the linear model.

Answers

Answer:

Option A The linear model on tar content accounts for 92.4% of the variability in nicotine content.

Step-by-step explanation:

R-square also known as coefficient of determination measures the variability in dependent variable explained by the linear relationship with independent variable.

The given scenario demonstrates that nicotine content is a dependent variable while tar content is an independent variable. So, the given R-square value 92.4% describes that 92.4% of variability in nicotine content is explained by the linear relationship with tar content. We can also write this as "The linear model on tar content accounts for 92.4% of the variability in nicotine content".

Final answer:

The Upper R squared or the coefficient of determination here represents the percentage of the variability in the nicotine content that can be explained by the tar content in the regression model, which in this case is 92.4%.

Explanation:

In this context, the meaning of Upper R squared is represented by option A. The linear model on tar content accounts for 92.4% of the variability in nicotine content. This indicates that 92.4% of the change in nicotine content can be explained by the amount of tar content based on the linear regression model used. This measure is also known as the coefficient of determination. Meanwhile, options B, C, and D are not correct interpretations of the R squared in this context. Both B and D wrongly relate the percentage to the predictability of the data points and option C incorrectly associates this percentage with the residual magnitude.

Learn more about Upper R squared here:

brainly.com/question/34151428

#SPJ3

Find the angle of rotation about the center of the regular pentagon that maps A to E

Answers

Answer:

C 288

Step-by-step explanation:

using counter clockwise rotation

360/5 x 4 =288

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