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2 years ago

Which equation accurately represents this statement? Select three options.

Mathematics

2 answers:

N76 [4]2 years ago

5 0

Answer:

X = 2

Step-by-step explanation:

4.9x - (-3) = 12.8

4.9x = 12.8 + (-3)

4.8x - 12.8 = -3

Can be three different forms

To solve:

4.9x = 12.8 - 3

4.9x = 9.8

x = 2

atroni [7]2 years ago

3 0

Complete question:

Which equation accurately represents this statement? Check all that apply.

Negative 3 less than 4.9 times a number, x, is the same as 12.8

A: -3-4.9x=12.8

B: 4.9x-(-3)=12.8

C: 3+4.9x=12.8

D: (4.9-3)x=12.8

E: 12.8=4.9x+3

Answer:

B: 4.9x-(-3)=12.8

C: 3+4.9x=12.8

E: 12.8=4.9x+3

Step-by-step explanation:

The word equation can be expressed mathematically as follows

negative 3 → -3

less than 4.9 times a number , x → 4.9 x - (-3)

is same as 12.8 → 4.9 x - (-3) = 12.8

The equation can be expressed as

4.9 x - (-3) = 12.8

when you open the bracket, you multiply -3 time - 1 . MInus times minus is equals to plus. so you get

4.9 x + 3 = 12.8

12.8 = 4.9x+3

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A wheat farmer cuts down the stalks of wheat and gathers them in 200 piles. The 200 gathered piles will be put on a truck. The t

denpristay [2]

Answer:

Check the explanation

Step-by-step explanation:

We want to estimate the total weight of grain on the field based on the data on a simple random sample of 5 piles out of 200. The population and sample sizes are N=200 & n=5 respectively.

1) Let Y_1,Y_2,...,Y_{200} be the weight of grain in the 200 piles and y_1,y_2,...,y_{5} be the weights of grain in the pile from the simple random sample.

We know, the sample mean is an unbiased estimator of the population mean. Therefore,

$\widehat{\mu}=\overline{y}=\frac{1}{5}\sum_{i=1}^{5}y_i=\frac{1}{5}(3.3+4.1+4.7+5.9+4.5)=4.5$

where \mu is the mean weight of grain for all the 200 piles.

Hence, the total grain weight of the population is

$\widehat{Y}=Y_1+Y_2+...+Y_{200}$

= $200\times \widehat{\mu}\: \: \: =200\times 4.5\: \: \: =900\, lbs$

2) To calculate a bound on the error of estimates, we need to find the sample standard deviation.

The sample standard deviation is

S= $\sqrt{\frac{1}{5-1}\sum_{i=1}^{5}(y_i-\overline{y})^2}\: \: \: =0.9486$

Then, the standard error of $\widehat{Y} is$

$\sigma_{\widehat{Y}} =\sqrt{\frac{N^2S^2}{n}\bigg(\frac{N-n}{N}\bigg)}\: \: \:$ =83.785

Hence, a 95% bound on the error of estimates is

$[\pm z_{0.025}\times \sigma_{\widehat{Y}}]\: \: \: =[\pm 1.96\times 83.875]\: \: \: =[\pm 164.395]$

3) Let x_1,x_2,...,x_5 denotes the total weight of the sampled piles.

Mean total weight of the sampled piles is

$\overline{x}=\frac{1}{5}\sum_{i=1}^{5}x_i=45$

The sample ratio is

$r=\frac{\overline{y}}{\overline{x}}=\frac{4.5}{45}$ =0.1 , this is also the estimate of the population ratio R= $\frac{\overline{Y}}{\overline{X}} .$

Therefore, the estimated total weight of grain in the population using ratio estimator is

$\widehat{Y}_R\: \: =r\times 8800\: \: =0.1\times 8800\: \: =880\,$ lbs

4) The variance of the ratio estimator is

var(r)= $\frac{N-n}{N}\frac{1}{n}\frac{1}{\mu_x^2}\frac{\sum_{i=1}^{5}(y_i-rx_i)^2}{n-1} , where \mu_x=8800/200=44lbs$

= $\frac{200-5}{200}\, \frac{1}{5}\: \frac{1}{44^2}\, \frac{0.2}{5-1}=0.000005$

Hence, the standard error of the estimate of the total population is

$\sigma_R=\sqrt{X^2 \: var(r)}\: \: \: =\sqrt{8800^2\times 0.000005}\: \: \:$ =21.556

Hence, a 95% bound on the error of estimates is

$[\pm z_{0.025}\times \sigma_{R}]\: \: \: =[\pm 1.96\times 21.556]\: \: \: =[\pm 42.25]$

8 0

2 years ago

Read 2 more answers

Explain why there are two sine ratios, two cosine ratios, and two tangent ratios for any right triangle

taurus [48]

Each angle has a sin, cos, and tan associated with it.
in a right angled triangle there are two other angles which each have ratios.

5 0

1 year ago

Read 2 more answers

A. One day Annie weighed 24 ounces more than Benjie, and Benjie weighed 3 1/4 pounds less than Carmen. How did Annie’s and Carme

Debora [2.8K]

<h2>Answer:</h2>

Let Annie's weight be = a

Let Benjie's weighs = b

Let Carmen's weight be = c

One day Annie weighed 24 ounces more than Benjie, equation forms:

$a=b+24$ ......(1)

Benjie weighed 3 1/4 pounds less than Carmen.

In ounces:

1 pound = 16 ounces

$\frac{13}{4}$ pounds = $\frac{13}{4}\times16=52$ ounces

$b=c-52$ or

$c=b+52$ ......(2)

Now adding (1) and (2), we get

a+b=b+24+c-52

=> $a=c-28$

This gives Annie weighs 28 ounces less than Carmen.

We cannot know anyone's actual weight, as we only know their relative weights.

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2 years ago

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored f

AnnZ [28]

Volume of cube=side³
ok, so you need to know the difference or sum of cubes
a³+b³=(a+b)(x²-xy+y²)
so

(4p)³+(2q²)³=
(4p+2q²)((4p)²-(4p)(2q²)+(2q²)²)=
(4p+2q²)(16p²-8pq²+4q⁴)

3rd option

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1 year ago

In what line do planes A and QRV intersect?

BabaBlast [244]

Answer:

Plane A and QRV intersection line is QR.

Explanation:

The plane QRV contains the rectangle QRVN. This rectangle intersects the plane A in the line QR.

Plane A and QRV intersection line is QR.

If one knows a specific line in one plane (for example, two points in the plane), and this line intersects the other plane, then its point of intersection.

Thus, it is on the line of intersection for the two planes.

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2 years ago