A bed frame normally weighs 60 pounds. A new,
stronger material increases the durability of the
frame but makes it weigh 30% more. How many
pounds does the new frame weigh?
F. 63
G. 66
H. 78
J. 90
K. 102

Answer:

\(AC = \frac{20}{3}\)

Step-by-step explanation:

Given

\(AB = 4\)

\(XY = 3\)

\(XZ = 5\)

Required

Find AC

ABC XYZ

To solve AC, we make use of the following equivalent ratios.

\(AB : AC = XY : XZ\)

This gives:

\(4 : AC = 3 : 5\)

Express as fraction

\(\frac{4 }{ AC }= \frac{3 }{ 5}\)

Cross multiply

\(3 * AC = 4 * 5\)

\(3 * AC = 20\)

Solve for AC

\(AC = \frac{20}{3}\)

Step-by-step explanation:

\( \frac{1}{4x} - \frac{2}{x} = 3 \\ \frac{1}{4x} - \frac{2}{x} \times \frac{4}{4} = 3 \\ \frac{1}{4x} - \frac{8}{4x} = 3 \\ \frac{1 - 8}{4x} = 3 \\ \frac{ - 7}{4x} = 3 \\ 4x = \frac{ - 7}{3} \\ x = \frac{ - 7}{12} \\ thank \: you\)

Answer:

\(→ \frac{1}{4x} - \frac{2}{x} = 3 \\ \frac{1}{4x} - \frac{(2 \times 4)}{(x \times 4)} = 3 \\ \frac{1}{4x} - \frac{8}{4x} = 3 \\ \frac{(1 - 8)}{4x} = 3 \\ \frac{( - 7)}{4x} = 3 \\ \frac{1}{x}= \frac{(3 \times 4)}{( - 7)} \\ \frac{1}{x}= \frac{12}{( - 7)} \\ \boxed{x = \frac{( - 7)}{12} }\)

The expanded form of log \((ab)^{2}\)  using the laws of the logarithm is 2log a + 2log b.

The logarithm is the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if \(b^x\) = n, which can be written as x = \(log_{b}\) n.

For example,  \(3^{2}\) = 9; therefore, 2 is the logarithm of 9 to base 3, or \(2 =log_{3} 9\)

Now, we will use the laws of the logarithm to expand the term log (ab)^2 as follows -

log \((ab)^{2}\)

= 2 log (ab)

Using the product property, we will get,

= 2(log a + log b)      

= 2log a + 2log b

Hence, the expanded form of log \((ab)^{2}\) is 2log a + 2log b.

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The complete question is -

Use the laws of the logarithm to expand the term log (ab)^2.

Answer:

B) Jet ski rental costs $20 initially plus $15 for each hour.

Step-by-step explanation:

The equation of a line has the following format:

\(y = mx+b\)

In which m is the slope, which having two points on the line, is given by the change in y divided by the change in x, and b is the y-intercept, which is the value of y when \(x = 0\).

Passes through point Y (0, 20):

This means that \(b = 20\). So

\(y = mx+20\)

Slope:

Through points (0,20) and (4,80). So

Change in y: 80 - 20 = 60

Change in x: 4 - 0 = 4

Slope: 60/4 = 15

So

\(y = 15x+20\)

Situation:

We want a situation in which we have a fixed fee of 20, and then for each unit of time or of the product, and increase of 15. So the correct option is B

Answer:

The correct answer is C.

Step-by-step explanation:

Answer: C. 102 cm

Step-by-step explanation:

I took the quiz on Edge, and it is correct.

iven:

here are givren the expression:

xplanation:

o find the coefficient of the given expression, we need to use the binomial expansion formula:

So,

From the formula of binomial expansion:

then,

After using the above formula in the given binomial, the expansion will be:

inal answer:

ence , the coefficient of the given term is shown below:

Answer: The future value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

FV = PMT * ( ( (1 + r)^n - 1) / r) * (1 + r)

where PMT = $300, r = 6%/12 = 0.05, and n = 10 years * 12 months/year = 120 months.

Substituting these values into the formula, we get:

FV = $300 * ( ( (1 + 0.05)^120 - 1) / 0.05) * (1 + 0.05)

FV = $300 * ( ( 1.05^120 - 1) / 0.05) * 1.05

FV = $300 * ( ( 2.704813829421526 - 1) / 0.05) * 1.05

FV = $300 * ( 1.704813829421526 / 0.05) * 1.05

FV = $300 * 34.09627658843153 * 1.05

FV = $52,113.63

Therefore, the future value of the annuity due is $52,113.63.

Step-by-step explanation:

Since y is directly proportional to x and y = 5 when x = 4, the value of y is equal to 10.

In Mathematics, a direct variation can be modeled by this mathematical expression:

y = kx

Where:

Based on the information provided above, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:

k = y/x

k = 5/4

Now, we can determine the value of y:

y = kx

y = 5/4 × 8

y = 10.

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The value of c in the triangle is (b) 5 units

From the question, we have the following parameters that can be used in our computation:

The right triangle

The length c is the hypotenuse of one of the triangles and can be calculated using the following Pythagoras theorem

c² = sum of squares of the legs

Using the above as a guide, we have the following:

c² = 3² + 4²

Evaluate

c² = 25

Take the square roots

c = 5

Hence, the hypotenuse of the right triangle is 5

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Answer:

Company B is cheaper by $180.

Step-by-step explanation:

just do 1,200 square feet x 0.15 = 180

Answer:

b as in big cat

Step-by-step explanation:

Answer:

slope  1/7

y intercept: (0, -67)

slope intercept form: y=1/7x - 61/7

Step-by-step explanation:

point slope form is

y+9=1/7 *(x+2)

Answer:

The  sampling distribution of the average cost of a root canal treatment in Riverside County is normal  with a mean of  $1,100  and  standard deviation of \(\sigma_{\= x} = \$ 17.67\)

Step-by-step explanation:

From the question we are told that

    The mean is \(\mu = \$ 1,100\)

      The standard deviation is  \(\sigma = \$ 50\)

     The  sample size is  n =  8

Generally the standard deviation of the mean of the sampling distribution is mathematically represented as

            \(\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }\)

=>        \(\sigma_{\= x} = \frac{50 }{\sqrt{8} }\)

=>        \(\sigma_{\= x} = \$ 17.67\)

Generally given that the sampling distribution of the fees in the nation as a whole is normal with a with the mean of $1,100  and  the SD of $50

Then the   \(\= x\)( sample mean of the country side ) is  normally distributed with a mean of  $1,100  and  standard deviation of \(\sigma_{\= x} = \$ 17.67\)

Answer: y = (-2/3)x - 3

Step-by-step explanation:

We'll be using y = mx + b

m = slope

b = y-intercept

Because we know this line will pass through -3, -1, we can input that.

y = mx + b

-1 = (-2/3)(-3) + b

-1 = 2 + b

b = -3

We can input that now to get the equation

y = (-2/3)x - 3

We know that the sum of the internal angles is equal to 180°, then we write and solve a linear equation to see that the missing angle is 94°.

Remember that for any triangle, we know that the sum of the interior angles is equal to 180°.

In this case we know that two of the angles have a measure of 62° and 24°, and if the third angle is x, then we can write the linear equation:

62° + 24° + x = 180°

To solve this we need to isolate x, we will get:

x = 180° - 24° - 62°

x = 94°

So the measure of the third interior angle is 94 degrees.

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The standard deviation by the given  probability distribution is 3.3412.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We are given that;

x P(x)

−5 0.17

−3 0.21

−1 0.09

3 0.23

5 0.23

7 0.07

Now,

To find the standard deviation, we need to use the formula:

standard deviation = sqrt[∑(x - μ)²P(x)]

where μ is the expected payout.

We have already calculated μ to be 0.76. Using this value and the given probabilities, we can calculate the standard deviation as:

standard deviation = sqrt[( (-5 - 0.76)² * 0.17) + ((-3 - 0.76)² * 0.21) + ((-1 - 0.76)² * 0.09) + ((3 - 0.76)² * 0.23) + ((5 - 0.76)² * 0.23) + ((7 - 0.76)² * 0.07)]

=3.3412

Therefore, by the given data the standard deviation will be 3.3412.

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Using the formula for the midpoint of the line with given points  A and B as the end points of the line, the coordinates of the point B is (6,-8).

To find the midpoint of a line segment, you must first find the coordinates of the two endpoints of the segment. Then, take the average of the x-coordinates and the y-coordinates to find the x and y coordinates of the midpoint. This can be done by adding the x-coordinates and y-coordinates of the two endpoints together and then dividing by 2.

What is the formula for finding the midpoint of a line segment?

The formula for finding the midpoint of a line segment is:

Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )

Where (x1,y1) and (x2,y2) are the coordinates of the two endpoints of the line segment.

Using the given coordinates of point A(8,-6) and the midpoint M(7,-7) of the line,  and using the midpoint formula for a line AB,

Midpoint(M) = \((\frac{x1+x2}{2},\frac{y1+y2}{2} )\)

where x1, y1 are coordinates of point A , and x2, y2 are the coordinates of point B

so , (7,-7) = \((\frac{8+x2}{2} , \frac{-6+y2}{2})\)

equating the corresponding points,

7 =(8+x2)/2

therefore, x2 = 6

and , -7 = (-6+y2)/2

therefore , y2 = -8

Hence the coordinates of B is , (x2,y2 ) = (6,-8)

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The expression with the correct coefficients in each block is given as follows:

20x³ + 0x² - 7x.

The functions in the context of this problem are defined as follows:

The operation is given as follows:

f(x)g(x) + h(x).

Hence, to obtain the resultant function, we apply the definitions into the operation and the simplify, applying the distributive property and combining the like terms, as follows:

4x(5x² - 4) + 9x = 20x³ - 16x + 9x = 20x³ - 7x.

As there is no x² term, the coefficient of zero multiplies the term x².

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The expression expressed as a difference is (a - 2) - (-7).

We have,

We can express a + 5 as a difference by subtracting a suitable term from it.

One way to do this is to subtract 2 and add 2, like this:

a + 5 = a + 5 - 2 + 2   (adding and subtracting 2)

     = (a - 2) + 7     (rearranging)

Now,

We can express a + 5 as the difference between a - 2 and -7, like this:

a + 5 = (a - 2) - (-7)

Thus,

The expression expressed as a difference is (a - 2) - (-7).

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Answer:

Step-by-step explanation:

Let's call the number of hotdogs sold "x". According to the problem, the number of sodas sold is three times the number of hotdogs sold, or 3x.

We know that the total number of sodas and hotdogs sold is 136. So we can set up an equation:

x + 3x = 136

Simplifying this equation, we get:

4x = 136

Dividing both sides by 4, we get:

x = 34

This means that 34 hotdogs were sold. To find the number of sodas sold, we can multiply the number of hotdogs sold by 3:

3x = 3(34) = 102

So, 102 sodas were sold.

Answer:

Verticle stretch

Step-by-step explanation:

it is vetically stretched by 2.

Answer:

It is the arithmetic sequence and the common ratio is 10

Step-by-step explanation:

It is arithmetic sequence

 This is because

-Geometric is multiplication

-arithmetic is addition  

----

Now the common ratio/difference is 10 as it adds 10 each time

4, 4+10 (14), 14+10 (24)

Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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The image for P(9, 1.5) after Translation is P'( 12, 1).

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

P(9, 1.5) with Translating Vector (3, -0.5).

So, Applying the Translation we get

P(9 + 3, 1.5 + (-0.5))

= P(12 , 1.5- 0.5)

= P(12, 1)

hence, the image is P'( 12, 1).

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In the question, we can draw the conclusion that, according to the formula, it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of \(415 miles\)per day.

A formula is a set of mathematical signs and figures that demonstrate how to solve a problem.

Formulas for calculating the volume of \(3D\) objects and formulas for measuring the perimeter and area of \(2D\) shapes are two examples.

A formula is a fact or a rule in mathematical symbols. In most cases, an equal sign connects two or more values. If you know the value of one, you can use a formula to calculate the value of another quantity.

We need to know the average pace at which they went to figure how long it would take to get from City A to City B at the same rate.

total distance / time taken = average speed

\(415 miles\) per day \(2075/ 5\), it would take them \(10\) days to get from City A to City B because

Time taken = \(2075/415\) per days \(= 5 days\)

Therefore it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of \(415 miles\)per day.

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Step-by-step explanation:

1. the claim here is that over 60 percents of the households living in ann harbor have pets.

null hypothesis;

h0: p≤0.60

alternative:

h1: p>0.60

2.

n is the size of the sample = 280

n(p) = 280 x 0.60 = 168 greater than 10

n(1-p) = 280(1-0.6) = 280 x 0.4 = 112  greater than 10

we use the normal dist since each of the above are greater than 10

3. n = 280

x = 182

x/n = 182/280

= 0.65

we get the test statistic z

z = \(\frac{0.65-0.6}{\sqrt{0.6*(1-0.6)/280} }\)

= \(\frac{0.05}{\sqrt{0.000857} }\)

=\(\frac{0.05}{0.02927}\)

≈ \(1.71\)

we get the p value = 1-p(z<1.71)

= 1-.9562

this gives 0.0438

4. we can see that 0.0438 < 0.10

so we conclude that over 60% of these households have at least one pet since we rejected h0.