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2 years ago

Find the value of g(7) for the function below. g(x) = 3x − 3

Mathematics

2 answers:

Anna11 [10]2 years ago

5 0

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Substitute 7 into 'x':

3(7) - 3

Solve:

g(7) = 18

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kakasveta [241]2 years ago

5 0

Answer: 18

Step-by-step explanation:

To find g(7) , we simply replace 7 by x

g(x) = 3x - 3

g(7) = 3(7) - 3

g(7) = 21 - 3

g(7) = 18

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A. 70 × g
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2 years ago

Five friends bake ginger bread and subsequently meet up for a tasting session. Each one gives one of his ginger

GenaCL600 [577]

Answer:

The five friends had 10 fingers to start with; one had two each

Step-by-step explanation:

The statement says each gave one of not all of his ginger in the toasting session.

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2 years ago

A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marin

djyliett [7]

Answer:

A) (7.6, 8.8)

which are the coordinates of the treasure.

Missing Problem Statement:

Given Options:

A) (11.4, 14.2)

B) (7.6, 8.8)

C) (5.7, 7.5)

D) (10.2, 12.6)

I have added the picture showing the traced map onto a coordinate plane to find exact location of treasure.

The coordinates of Tree are (16,21)

Coordinates of rock are (3,2)

Step-by-step explanation:

Let,

Coordinates of treasure be (a,b)

$d_{1}$ = distance from tree to treasure

$d_{2}$ =distance from rock to treasure

$d_{1}=\sqrt{(16-x)^2 + (21-y)^2}$

$d_{2}=\sqrt{x\2 + (y-2)^2}$

Given ratio between rock and tree, $\frac{d_{2}}{ d_{1}}=\frac{5}{9}$ = 0.55_______(Equation.1)

which will be used to locate the treasure.

Now we just need to cross check by putting the coordinates given in the options one by one to find out value of $d_{1}$ , $d_{2}$ and checking if it satisfies the Equation 1.

Check (A) (11.4, 14.2)

$d_{2}$ = 14.8, $d_{1}$ = 8.2,

$\frac{d_{2}}{ d_{1}}$ = 1.8

Check (C) (5.7, 7.5)

$d_{2}$ = 6.13, $d_{1}$ = 16.98,

$\frac{d_{2}}{ d_{1}}$ = 0.36

Check (D) (10.2, 12.6)

$d_{2}$ = 12.8, $d_{1}$ = 10.2,

$\frac{d_{2}}{ d_{1}}$ = 1.25

Check (B) (7.6, 8.8)

$d_{2}$ = 8.2, $d_{1}$ = 14.8,

$\frac{d_{2}}{ d_{1}}$ = 0.55

Which satisfies Equation 1, such that ratio between rock and tree is 5:9 or $\frac{d_{2}}{ d_{1}}=\frac{5}{9}$ = 0.55

So, the coordinates of the treasure are (B) (7.6, 8.8)

7 0

2 years ago

Read 2 more answers

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

1. What is m∠CAD?

bulgar [2K]

< CAD = 100....if u add < ACB + < CBA u get < CAD
================
< DAB = 125 and < ACB = 30

if DAB = 125.....then BAC = 180 - 125 = 55
and all 3 interior angles of a triangle = 180
< BAC + < ACB + < ABC = 180
55 + 30 + < ABC = 180
85 + < ABC = 180
< ABC = 180 - 85
< ABC = 95 <===

6 0

2 years ago

Read 2 more answers