what is 4.2j+6.7j-5j-5​

Answer:

10a+16...hope this helps!

Step-by-step explanation:

The answer is 6.85.

Consider, x-y axis, and side of equilateral triangle is ' a '.

Given,

\($$\begin{aligned}&A P=3 \text { units } \\&B P=2 \text { units } \\&C P=4 \text { units }\end{aligned}$$\)

Let x and y are point in x-y axis.

Using, distance formula here

\($A P^{2}=(x-0)^{2}+(y-0)^{2}$\)

\($3^{2}=x^{2}+y^{2}$\)

\($x^{2}+y^{2}=$\)__________(i)

\($p c^{2}=(x-a)^{2}+(y-0)^{2}$$4^{2}=x^{2}-2 a x+a^{2}+y^{2}$\)

from (i)

\($16=x^{2} 9-2 a x+a^{2}$\)

\($2 a x=a^{2}+9-16$\)

\($\left[x=\frac{\left(a^{2}-7\right)}{2 a}\right]$\)

\($B p^{2}=\left(x-\frac{a}{2}\right)^{2}+\left(y-\frac{\sqrt{3}}{2} a\right)^{2}$\)

\($2^{2}=x^{2}-a x+\frac{a^{2}}{4}+y^{2}-\sqrt{3} a b y+\frac{3}{4} a^{2}$\)

\($4=\left(x^{2}+y^{2}\right)+\frac{a^{2}+3 a^{2}}{4}-a\left(\frac{a^{2}-7}{2 a}\right)-\sqrt{3} a y$\)

from (i)

\($4=9+a^{2}-a^{2}+7-\sqrt{3} a y$\)

\($\sqrt{3} a y=16-4$\)

put x and y in equarion_______(i)

\($\left(\frac{12}{\sqrt{3} a}\right)^{2}+\left(\frac{a^{2}-7}{2 a}\right)^{2}=9$\)

\($\frac{144}{3 a^{2}}+\frac{\left(a^{2}-7\right)^{2}}{4 a^{2}}=9$\)

\($144 \times 4+3\left(a^{2}-7\right)^{2}=12 \times 9 a^{2}$\)

\($576+3\left(a^{2}-7\right)^{2}=108 a^{2}$\)

\(put $a^{2}=t$$$576+3(t-7)^{2}=108 t$$\)

\($\begin{aligned} 576+3\left(t^{2}-14 t+49\right) &=108 t \\ 576+3 t^{2}-42 t+147 &=108 t \end{aligned}$\)

\($3 t^{2}-150 t+429=0$$t^{2}-50 t+143=0$$t=50 \pm \sqrt{50^{2}-4 \times 143}$\)

\(t=\frac{50 \pm \sqrt{1928}}{2}t=\frac{50 \pm 43.91}{2}\)

\(t=\frac{50 \pm 43.91}{2}\\t=46.9545, \quad t=3.0455\)

\($\begin{array}{ll}a^{2}=46.9545, \\ a=\sqrt{46.9545}, & a^{2}=3.0455 \\ a, a=1.745\end{array}$\)

\($a=6.85$\)

for this point P is outside Therefore, it is not consider as solution (because in question inside point ls mention)

\(a=6.85 units\)

What is equilateral triangle?

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Answer:

d. h(x) = 4x + 48

Step-by-step explanation:

\(f(x) = \frac{1}{4} x - 12\)

\(y = \frac{1}{4} x - 12\)

\(x = \frac{1}{4} y - 12\)

\( \frac{1}{4} y - 12 = x = 4( \frac{1}{4} y - 12) = 4x\)

\(4 \times \frac{1}{4} y - 4 \times 12 = 4x\)

\(y - 48 = 4x\)

\(y = 4x + 48\)

\(\boxed{\green{= h(x) = 4x + 48}}\)

Answer: x=7

Step-by-step explanation:

(3x+6)+(8x+7)=90

(3x+6)+(8x+7)+90=180

SOLVE THE SYSTEM OF EQUATIONS

YOU GET 7

The question is incomplete. The complete question is :

Cylinders A and B are similar. The length of the cylinder A is 4 mm and the length of cylinder B is 6 mm. The volume of cylinder A is 20mm3. Calculate the volume of cylinder B.

Answer:

67.5 \(mm^3\)

Step-by-step explanation:

Given that :

Cylinder A and cylinder B are similar.

Let volume of cylinder A = 20 \(mm^3\)

We know the volume of a cylinder is given by V = \($\pi r^2 h$\)

where, r is the radius of the cylinder

            h is the height of the cylinder

We have to find the scale factor.

The length scale factor is = \($\frac{6}{4}$\)

                                          \($=\frac{3}{2}$\)

Area scale factor \($=\left(\frac{3}{2}\right)^2$\)

                           \($=\frac{9}{4}$\)

∴ Volume scale factor \($=\left(\frac{3}{2}\right)^3$\)

                                     \($=\frac{27}{8}$\)

Therefore, the volume of cylinder B is \($=20 \times \frac{27}{8}$\)

                                                               = 67.5 \(mm^3\)

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Answer:

24

Step-by-step explanation:

We have a system of equations, so we can start with the second equation:

\(x-y=2\)

And move y to the other side to isolate x:

\(x=2+y\)

Now we can replace x into the first equation:

\((2+y)^{2} -y^{2} =48\\ (2+y)(2+y)-y^{2} =48\\ 4+4y+y^{2} -y^{2} =48\)

Notice that we can cancel out the y squared terms:

\(4+4y=48\\ 4y=44\\ y=11\)

Now we just need to find x by replacing y into the second equation:

\(x-11=2\\ x=13\)

And finally, add them:

\(x+y=11+13\\ x+y=24\)

Hope this helps.

Answer:

x= 13

y=11

x^2 - y^2 = 48        and       x - y = 2

                                           x = 2 + y

(2 + y)^2 - y^2 = 48

(2 + y) (2 + y) - y^2 = 4

(4 + 2y +2y + y^2) -y^2 = 48

4 + 4y + y^2 - y^2 = 48

4 + 4y = 48

4y = 48 -4

4y = 44

y= 44/4

y= 11

Plug y back into the original equation:

x^2 - y^2 = 48

x^2 - 11^2 = 48

x^2 - 121 = 48

x^2 = 121 + 48

x^2 = 169

The square root of 169 is 13

So x= 13

x + y

13 + 11 = 24

The inequality for sec (x) < cot (x) is;  π/2 < x < π

We are given that;

We want to find the intervals that the trigonometric inequality sec (x) < cot (x) always hold true.

This can also be expressed as;

1/cos (x) < 1/tan (x)

Now, this can happen only in the quadrant where tan (x) is negative and cos x is positive which is in fourth quadrant where;

π/2 < x < π

The inequality for sec (x) < cot (x) is;  π/2 < x < π

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Answer:

C on edge 22 for Pre-Calculus

Step-by-step explanation:

pi < x< 3pi/2

I retook the unit test, put C, and got a 100. I promise it's right

Answer:

12 Miles is the answer! Hope you do Great!

Step-by-step explanation:

Answer:

05 units up and down

Step-by-step explanation:

hope this hepled luv!

The phrase that best describes the translation from the graph y = 2x^2 to the graph of y = 2x^2 + 5 is "5 units up".

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

Adding a constant term to a function vertically shifts its graph up or down, depending on the sign of the constant.

In this case, the constant term is positive (+5), which means that the graph of y = 2x² + 5 is shifted upward by 5 units compared to the graph of y = 2x².

Therefore, the correct phrase is "5 units up".

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Justin"s heart rate decreased 3 beats per minute for each of next 4 minutes

Let his heart rate be be 1

For the first minutes

1 minute his heart rate was 1 - 3 = -2

This is because the heart rate is decreasing 3 beats per minutes

2minutes later, his heart beat will be -2 -3

-2 - 3 = -5

3 minutes later, his heart beat will be -5 - 3

-5 - 3 = -8

4 minutes later, -8 - 3

-8 - 3 = -11

Change = Final heart beat - initial heart beat / initial heart beat

Change = -11 -2 / -2

Change = -13/-2

Change = 13/2

= 6.5

The  ratio of the lateral area of cylinder A to the lateral area of cylinder B is 3:1.

The ratio of the lateral area of cylinder A to the lateral area of cylinder B can be found by comparing the corresponding sides.

The lateral area of a cylinder is given by the formula: 2πrh.

Let's denote the radius of cylinder B as r, and the radius of cylinder A as 3r (since the radius of A is 3 times the radius of B).

The height of the cylinders does not affect the ratio of their lateral areas, as long as the ratios of their radii remain the same.

Now, we can calculate the ratio of the lateral area of A to the lateral area of B:

Ratio = (Lateral area of A) / (Lateral area of B)

Ratio = (2π(3r)h) / (2πrh)

Ratio = (3r h) / (r h)

Ratio = 3r / r

Ratio = 3

Therefore, the ratio of the lateral area of cylinder A to the lateral area of cylinder B is 3:1.

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The mean of the given fuel prices data set is $4.61 with a standard deviation of $1.62.

To calculate the mean and standard deviation in Excel, you can use the following functions:

Mean: The AVERAGE function calculates the mean of a range of values. In this case, enter "=AVERAGE(A1:A30)" in an Excel cell, assuming the data is in cells A1 to A30.

Standard Deviation: The STDEV.S function calculates the standard deviation of a range of values. Enter "=STDEV.S(A1:A30)" in an Excel cell to calculate the standard deviation of the data set.

Using the mean ($4.61) and standard deviation ($1.62), we can now proceed to calculate the Confidence Interval.

The Confidence Interval can be determined using the formula: E = Z * (σ / √n)

In the formula, Z is the z-score corresponding to the desired level of confidence (e.g., 95% confidence corresponds to a z-score of approximately 1.96), σ is the population standard deviation (which can be estimated using the sample standard deviation in this case), and n is the sample size.

Let's assume we want a 95% confidence interval for the data set with a sample size of 30. We can use the formula "=CONFIDENCE.NORM(0.05, STDEV, 30)" in an Excel cell to calculate the E value.

Substituting the values into the formula, we get E = 1.96 * (1.62 / √30) ≈ 0.595.

Now, we can set up the confidence interval using the mean and E value:

Confidence Interval = (mean - E, mean + E)

Confidence Interval = ($4.61 - $0.595, $4.61 + $0.595)

Confidence Interval = ($4.015, $5.205)

Therefore, the 95% Confidence Interval for the given fuel prices data set is approximately $4.015 to $5.205.

In summary, the mean of the fuel prices data set is $4.61 with a standard deviation of $1.62. The 95% Confidence Interval for the data is approximately $4.015 to $5.205.

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Answer:

correct answer is A

Step-by-step explanation:

edge 2022

Step-by-step explanation:

I'm assuming you mean:

(4 - 2) / (-5 - 2)

First, simplify the numerator:

4 - 2 = 2

Next, simplify the denominator:

-5 - 2 = -7

Now, substitute the simplified numerator and denominator into the expression:

(4 - 2) / (-5 - 2) = 2 / (-7)

This fraction can be simplified by dividing numerator and denominator by their greatest common factor, which is 1 in this case:

2 / (-7) = -2/7

Therefore, (4 - 2) / (-5 - 2) = -2/7.

Answer:

ANother filthy£50

Step-by-step explanation:

Answer:

\((2 \times 7) - (9 \times 6) = - 40\)

Answer:

3/4

Step-by-step explanation:

6/8 = 3/4

Answer:

D

Step-by-step explanation:

You need to solve the equation so that it looks like y = mb + b

So -15y = -5x + 105, then divide both sides by -15 so y = -5/-15 x + 105/-15

y = \(\frac{1}{3}\) x  - 7

The polar coordinates are solved and the functions are:

a) r(θ) = f(|θ|)

b) r(θ) = f(θ + π)

c) r(θ) = -f(θ)

Given data:

In polar coordinates, a point is represented by the pair (r, θ), where r is the distance from the origin to the point and θ is the angle formed with the positive x-axis in the counterclockwise direction. To describe functions with specific symmetries in polar coordinates, we use the following:

a)

Symmetry with respect to only the x-axis:

For a function with symmetry with respect to the x-axis, the value of r is the same for angles θ and -θ. In other words, the function is even with respect to the polar angle.

Formula: r(θ) = f(|θ|)

Example: r(θ) = 2 + cos(|θ|)

b)

Symmetry with respect to only the y-axis:

For a function with symmetry with respect to the y-axis, the value of r is the same for angles θ and θ + π. In other words, the function is even with respect to the polar angle plus π.

Formula: r(θ) = f(θ + π)

Example: r(θ) = 3 + sin(θ + π)

c)

Symmetry with respect to the origin:

For a function with symmetry with respect to the origin, the value of r is the same for angles θ and θ + π. In other words, the function is odd with respect to the polar angle.

Formula: r(θ) = -f(θ)

Example: r(θ) = 4 - 2sin(θ)

To draw the graph of each function, you would plot points for different values of θ and connect them to create the polar graph. Note that the graphs for (a) and (b) will look the same since they both have symmetry with respect to the x-axis, and the graphs for (c) will look different as it has symmetry with respect to the origin.

Hence, the polar coordinates are solved.

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Answer:

25 and 1/3

Step-by-step explanation:

The population density for each animal is given as follows:

The population density is calculated as the division of the total population by the total area.

The area for this problem is given as follows:

2.22 million acres = 2,220,000 acres.

Hence the densities are given as follows:

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Answer:

180

Step-by-step explanation:

5(2)^2 (3)^3

5(4) (27)

4(27) = 108

5(108) = 540*

Answer:

c and b and a

Step-by-step explanation:

The store should charge a price between ($0, $0.94] to sell at least 625 pads each week. The store should charge a price between ($0, $1.75) to sell more than 300 pads each week. The store should charge a price between ($2.00, $2.50) to sell less than 200 pads each week. The store should charge a price between [$1.31, $2.50) to sell at most 475 pads each week.

a)

In order to solve part a of the problem, we need to set our equation as an inequality. Part a asks us to find the price the store should charge to sell at least 625 pads each week. The word at least gives us a clue on what symbol to use. In this case we should use the \(\leq\) symbol, like this:

\(625\leq 1000-400p\)

and now we can solve the inequality, we can start by switching places between the 625 and the 400p so we get:

\(400p\leq 1000-625\)

\(400p\leq 375\)

and we divide both sides into 400, so we get:

\(p\leq \frac{375}{400}\)

\(p\leq $0.94\)

So this can be rewritten in interval notation like this:

($0, $0.94] The price they should charge can be located between those two values.

b)

In order to solve part b of the problem, we need to set our equation as an inequality. Part b asks us to find the price the store should charge to sell at more than 300 pads each week. The word more than gives us a clue on what symbol to use. In this case we should use the < symbol, like this:

\(300< 1000-400p\)

and now we can solve the equation, we can start by switching places between the 300 and the 400p so we get:

\(400p< 1000-300\)

\(400p< 700\)

and we divide both sides into 400, so we get:

\(p< \frac{700}{400}\)

\(p< $1.75\)

So this can be rewritten in interval notation like this:

($0, $1.75) The price they should charge can be located between those two values.

c)

In order to solve part c of the problem, we need to set our equation as an inequality. Part c asks us to find the price the store should charge to sell less than 200 pads each week. The word less than gives us a clue on what symbol to use. In this case we should use the > symbol, like this:

\(200> 1000-400p\)

and now we can solve the inequality, we can start by switching places between the 200 and the 400p so we get:

\(400p> 1000-200\)

\(400p> 800\)

and we divide both sides into 400, so we get:

\(p> \frac{800}{400}\)

\(p> $2.00\)

at this point we need to know what the maximum price the store can charge is. We can do so by setting the equation equal to zero and solve for p, so we get:

0<1000-400p

so we can now move the 400p to the other side of the equation, so we get:

400p<1000

and divide both sides into 400 so we get:

\(p<\frac{1000}{400}\)

which simplifies to:

p<$2.50

if the store charges more than $2.50 they will not sell any item at all.

So this can be rewritten in interval notation like this:

($2.00, $2.50) The price they should charge can be located between those two values to sell less than 200 pads each week.

d)

In order to solve part d of the problem, we need to set our equation as an inequality. Part d asks us to find the price the store should charge to sell at most 475 pads each week. The word at most gives us a clue on what symbol to use. In this case we should use the \(\geq\) symbol, like this:

\(475\geq 1000-400p\)

and now we can solve the inequality, we can start by switching places between the 475 and the 400p so we get:

\(400p\geq 1000-475\)

\(400p\geq 525\)

and we divide both sides into 400, so we get:

\(p\geq \frac{525}{400}\)

\(p\geq $1.31\)

So this can be rewritten in interval notation like this:

[$1.31, $2.50) The price they should charge can be located between those two values to sell 475 pads at most each week.

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The total number of students surveyed is x = 126√70 ≈ 43

The problem requires that we find the total number of students surveyed. Suppose the total number of students surveyed was x.

From the problem, it is given that: 6 students prefer to work in groups for every 8 students who prefer to work individually.

Thus, if we use the ratio scale, the ratio of the number of students who prefer to work in groups to those who prefer to work individually is 6:8 or 6/8.

This can be simplified by dividing both the numerator and the denominator by 2 to get 3/4 or 0.75 in decimal form.

Thus, for every 3 students who prefer to work in groups, 4 prefer to work individually. Hence, the fraction of students who prefer to work in groups is 3/(3+4) = 3/7.

Since the number of students who prefer to work in groups is 4,200, we can write the fraction of students who prefer to work in groups as 4,200/x.
Equating both expressions for the fraction of students who prefer to work in groups, we have:4,200/x = 3/7.

Multiplying both sides of the equation by x and then by 7, we get:4,200 x 7 / 3 = x².

Simplifying, we get:x = sqrt(4,200 x 7 x 3) = 126√70.

Thus, the total number of students surveyed is x = 126√70 ≈ 430.

The total number of students surveyed is 126√70 ≈ 430.

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The  transformation of \(\(y= \frac{x^{4} }{6x+6}\)\) graph is compressed by a factor of 2.

The function is a rational function in which the numerator is a degree 4 polynomial, and the denominator is a degree 1 polynomial.

Rational functions are in the form of \(\(f(x) = \frac{p(x)}{q(x)}\)\), where p(x) and q(x) are polynomial functions and the degree of p(x) is less than the degree of q(x).

To transform a graph of a function, one can translate, stretch, or reflect it.

Here are some of the transformations of the function \(\(y= \frac{x^{4} }{6x+6}\)\)

Vertical Shift: To get the new graph, we add or subtract a constant from the function.

When f(x) is replaced with f(x) + k, we get a graph that is k units above the graph of f(x). In this case, if we subtract 2 from the equation, we get the following equation:

\(y = (x^4) / (6x+6) - 2\)

This means that the graph of the function is shifted 2 units downwards.

Horizontal Shift: To get the new graph, we add or subtract a constant to the variable.

When f(x+c) is replaced with f(x), the graph is shifted c units to the left.

When f(x-c) is replaced with f(x), the graph is shifted c units to the right.

In this case, we can shift the graph by substituting x-2 for x in the function.

The new function is: \(y = ((x-2)^4) / (6(x-2)+6)\)

This means that the graph is shifted 2 units to the right.

Vertical Stretch/Compression: When a constant is multiplied to the function, the graph is vertically stretched or compressed.

In this case, if the function is multiplied by 2, we get the following function:

\(y = 2(x^4) / (6x+6)\)

This means that the graph is compressed by a factor of 2.

It can also be stretched by dividing the function by a constant.

Horizontal Stretch/Compression:

When a constant is multiplied to the variable of the function, the graph is horizontally stretched or compressed. In this case, if the variable is divided by 2, we get the following function:

\(y = (x^4) / (3x+3)\)

This means that the graph is compressed by a factor of 2.

It can also be stretched by multiplying the variable by a constant.

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The difference in the dollar value of Assistantship (Stipend) between art and science fields with  standard errors is equal to 1.214.

Mean      24041.62203                 25952.36501

Sample mean difference between Assistantship (stipend) in arts and science is equal to

=  $25952.36501 - $24041.62203

= $1910.74298.

Hypothesized mean difference is 0 (there is no difference in stipend between the two fields).

Variance        621483.0801            615193.5853

Sample size    521                             479

Standard error of the difference is,

=√[(variance in arts / sample size in arts) + (variance in science / sample size in science)]

= √[(615193.5853 / 479) + (621483.0801 / 521)]

= $49.77

t-statistic

= (sample mean difference - hypothesized mean difference) / standard error of the difference

Substitute the values into the t-statistic formula,

⇒ t-statistic = ($1910.74298 - 0) / $49.77

⇒ t-statistic = 38.39

t-critical value for a two-tailed test with 992 degrees of freedom at a significance level of 0.05 is 1.9624.

t-statistic (38.39) > t-critical value (1.9624)

⇒Reject the null hypothesis that there is no difference in stipend between the two fields.

standard errors

= t-statistic / √(sample size)

= 38.39 / √(479 + 521)

= 38.39 /31.62

=1.214

Therefore,  the difference in the dollar value of Assistantship (Stipend) between these two fields is 1.214 standard errors away from the hypothesized difference.

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Answer:

Step-by-step explanation: