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3 years ago

Translate the following into an algebraic expression: A number is 30% of 20% of the number x.

Mathematics

1 answer:

bezimeni [28]3 years ago

4 0

Answer: 0.06x

Step-by-step explanation:

An algebraic expression is an expression consist of integer constants, variables, and algebraic operations.

The given statement: A number is 30% of 20% of the number x.

The required algebraic expression would be:

30% of 20% of x

$=\dfrac{30}{100}\times \dfrac{20}{100}\times x$ [we divide a percentage by 100 to convert it into decimal]

$=\dfrac{6}{100}\times x\\\\=0.06x$

Hence, the required algebraic expression would be :

0.06x

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The number of equally sized spaces needed between minus−1 and 0 is

JulsSmile [24]

One pace because -1 plus 1 is 0

5 0

3 years ago

One line passes through the points \blueD{(-3,-1)}(−3,−1)start color #11accd, (, minus, 3, comma, minus, 1, ), end color #11accd

mart [117]

Answer:

The lines are perpendicular

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

Remember that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Find the slope of the first line

we have the points

(-3,-1) and (1,-9)

substitute in the formula

$m_1=\frac{-9+1}{1+3}$

$m_1=\frac{-8}{4}$

$m_1=-2$

Find the slope of the second line

we have the points

(1,4) and (5,6)

substitute in the formula

$m_2=\frac{6-4}{5-1}$

$m_2=\frac{2}{4}$

Simplify

$m_2=\frac{1}{2}$

Compare the slopes

$m_1=-2$

$m_2=\frac{1}{2}$

Find out the product

$m_1*m_2=(-2)(\frac{1}{2})=-1$

therefore

The lines are perpendicular

8 0

3 years ago

Read 2 more answers

Estimate the tax on shoes that cost $68.50 when the sales tax rate is 8.25%.

Bond [772]

It would cost $74.15 for the shoes

8 0

3 years ago

Bastien, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. Th

alexira [117]

Answer:

We conclude that the the manufacturer's advertising campaign is not correct.

P-value of test = 0.067.

Step-by-step explanation:

We are given that an independent testing service road-tested 36 of the automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 6 miles per gallon.

We have to conduct a test to determine whether or not the manufacturer's advertising campaign is legitimate.

Let $\mu$ = population average gasoline of new small cars in highway driving.

SO, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 50 miles per gallon {means that the manufacturer's advertising campaign is not correct}

Alternate Hypothesis, $H_A$ : $\mu$ > 50 miles per gallon {means that the manufacturer's advertising campaign is correct}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average gasoline = 51.5 miles per gallon

$\sigma$ = population standard deviation = 6 miles per gallon

n = sample of automobiles = 36

So, test statistics = $\frac{51.5-50}{\frac{6}{\sqrt{36} } }$

= 1.50

Now at 0.05 significance level, the z table gives critical value of 1.6449 for right-tailed test. Since our test statistics is less than the critical values of z as 1.50 < 1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Also, P-value is given by the following formula;

P-value = P(Z > 1.50) = 1 - P(Z $\leq$ 1.50)

= 1 - 0.93319 = 0.067 or 6.7%

Therefore, we conclude that the the manufacturer's advertising campaign is not correct as its new small cars average less than or equal to 50 miles per gallon in highway driving.

3 0

3 years ago

In pentagon $MATHS$, $\angle M \cong \angle T \cong \angle H$ and $\angle A$ is supplementary to $\angle S$. How many degrees ar

gavmur [86]

Answer:

H = 120°

Step-by-step explanation:

The sum of the internal angles of a polygon with n sides is given by the formula:

S = (n-2)*180

So, for a pentagon, we have n = 5, then:

S = (5-2)*180 = 540°

So we have that:

M + A + T + H + S = 540° (eq1)

M = T = H (eq2)

A + S = 180° (eq3)

Using the second and third equation in the first one, we have:

H + H + H + 180 = 540

3H = 360

H = 120°

3 0

4 years ago