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3 years ago

Analyze the diagram below and complete the instruction that follow.

Mathematics

2 answers:

Gnoma [55]3 years ago

5 0

Answer:

Step-by-step explanation:

We are given a diagram which we are to analyze and and solve for x.

We can see the a straight line is intersected by another line thus forming two angles which are supplementary. It means that the sum of these angles is equal to 180 degree.

So we can write them as:

$( 7 x - 3 ) + ( 12 x - 7 ) = 180 \\\\ 12 x + 7 x = 180 + 3 + 7 \\\\ 19 x = 190 \\\\ x = \frac { 190 } { 19 }\\\\ x = 10$

Therefore, the correct answer option is 10.

monitta3 years ago

3 0

Answer:

x=10

Step-by-step explanation:

The two angles form a straight line so they add to 180 degrees

7x-3 + 12x-7 = 180

Combine like terms

19x-10 = 180

Add 10 to each side

19x-10+10 = 180+10

19x = 190

Divide by 19

19x/19 = 190/19

x= 10

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1/4x – 2 = 3/8 Please show an equation and work. :)

Julli [10]

1/4x - 2 = 3/8

First, to start solving this, we can rearrange our fraction. Let's take 1/4x and change it to x/4. Why? Well, a variable can also be considered as the number 1.
$\frac{x}{4} - 2 = \frac{3}{8}$

Second, now we can continue solving for our variable (x). Let's add 2 to each side.
$\frac{x}{4} = \frac{3}{8} + 2$

Third, let's simplify 3/8 + 2. (3/8 + 2 = 2.375 =19/8)
$\frac{x}{4} = \frac{19}{8}$

Fourth, continue trying to get the variable by itself. Multiply each side by 4.
$x = \frac{19}{8} \times 4$

Fifth, let's simplify 19/8 × 4. This is simple. Leave the denominator be and just do 19 × 4, which equals 76.
$x = \frac{76}{8}$

Sixth, our final step is to simplify our fraction. To do so, we will need to list the factors of the numerator and denominator and find the greatest common factor (GCF).

Factors of 76: 1, 2, 4, 19, 38, 76
Factors of 8: 1, 2, 4, 8

Since 4 is our first common factor, it is considered our GCF.

Seventh, now let's divide. Divide both the numerator and denominator by the GCF (4) to create our new simplified fraction.
$76 \div 4 = 19 \\ 8 \div 4 = 2$

Answer in fraction form: $\fbox {x = 19/2}$
Answer in decimal form: $\fbox {x = 9.5}$

8 0

3 years ago

According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating

Natali [406]

Answer:

a) Null and alternative hypothesis

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

b) Test statistic t=-1.565

P-value = 0.0612

NOTE: the sample size is n=65.

c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

d) Null and alternative hypothesis

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

Test statistic t=-1.565

Critical value tc=-1.669

t>tc --> Do not reject H0

Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Then, the null and alternative hypothesis are:

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

The significance level is 0.05.

The sample has a size n=65.

The sample mean is M=30.15.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{65}}=1.4884$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{30.15-32.48}{1.4884}=\dfrac{-2.33}{1.4884}=-1.565$

The degrees of freedom for this sample size are:

$df=n-1=65-1=64$

This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Critical value approach

At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.

As the test statistic is greater than the critical value, it falls in the acceptance region.

The null hypothesis failed to be rejected.

6 0

3 years ago

Neena has 54 smiley faces stickers and 36 glittery stickers. She wants to divide the stickers evenly among her friends

Ilia_Sergeevich [38]

90 divided by X (x is the number of friends which the question did not provide)

4 0

3 years ago

Read 2 more answers

50 cases in 44 minutes equals how many cases in 60 minutes

Blizzard [7]

To solve this, set up a proportion, crossmultiply, and solve for x.

Let x = the unknown amount of cases in 60 minutes.

$\frac{50}{44} = \frac{x}{60}$
44x = 50(60)
44x = 3000

Divide both sides by 44 to isolate variable x
x = 3000 / 44
x ≈ 68.1818 (the 18s repeat forever)

Rounding to the closest case and assuming the rate stays constant, you would get approximately 68 cases in 60 minutes. If you need not round to the nearest case, you would get approximately 68.18 cases in 60 minutes.

4 0

3 years ago

A stock worth $42 at the beginning of the day. The stock depreciates 15% every hour. How much will the stock be worth after 7 ho

liubo4ka [24]

Answer:

14.46

Step-by-step explanation:

first hour: 35.7

2 hour: 30.34

3 hour: 25.79

4 hour: 21.93

5 hour: 18.64

6 hour:15.85

7 hour:14.46

7 0

3 years ago