The distance between -7 and 2 on the number line is _____. 5 9 -5 10

The total cost of the laptop $778.63

The sales tax rate is 8.75%

= 8.75/100

= 0.0875

The listed price of the laptop is 715.98

= 0.0875 × 715.98

= 62.65

The total cost can be calculated as follows

= 62.65 + 715.98

= 778.63

Hence the total cost of the laptop with sales tax included is $778.63

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(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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The vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

Given equation :

y=(x−2)2−8

y = 2x - 4 - 8

= 2x - 12

The final equation is y = 2x - 12.

Compare this equation with slope and y-intercept formula :

y = mx+c

So that c = -12

The value of y-intercept according to the solution is -12.

To find the vertex. Let's assume x=0; Substitute in the equation

y = 2(0) -12

y = -12

The first vertex will be (0, -12)

If x = 1; y = 2(1) -12

y = -10

Then the second vertex will be (1, -10).

Hence, the vertex of the given equation is (0,12) and (1, -10). The value of y-intercept will be -12.

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Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

Step-by-step explanation:

If we have 7 vegetables, and we had to put 4 of them in my soup.

Subtract, and don't use does.

so for example

tomato

carrot

broccoli

onion

blah

blah

blah

we got to pick tomato carrot onion and broccoli

do not use blah since they we only need 4. not 3.

a = amount invested at 4%

how much is 4% of "a"? (4/100) * "a", namely 0.04a.

b = amount invested at 10%

how much is 10% of "b"? (10/100) * "b", namely 0.10b.

c = amount invested at 14%

how much is 14% of "c"? (14/100) * "c", namely 0.14c.

we know the total amount invested is 6000, so whatever "a" and "b" and "c" might be, we know that a + b +c = 6000.

we also know that the yielded amount in interest is $652, so if we simply add their interest, that'd be 0.04a + 0.10b + 0.14c.

the combined amount of "a" and "b" is simply a + b, and we also know that "c" is that much plus 200, namely "c = a + b + 200".

\(a+b+c=6000\hspace{5em}\underline{c=a+b+200} \\\\\\ a+b+\stackrel{c}{(a+b+200)}=6000\implies 2a+2b+200=6000\implies 2a+2b=5800 \\\\\\ 2b=5800-2a\implies b=\cfrac{5800-2a}{2}\implies \boxed{b=2900-a} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{c=a+b+200}\implies \stackrel{substituting}{c=a+(\underset{b}{2900-a})+200}\implies c=a+2900-a+200 \\\\\\ c=2900+200\implies {\Large \begin{array}{llll} c=3100 \end{array}} \\\\[-0.35em] ~\dotfill\)

\(0.04a+0.10b+0.14c=652\implies \stackrel{\textit{substituting}}{0.04a+0.10(\underset{b}{2900-a})+0.14(\underset{c}{3100})}=652 \\\\\\ 0.04a+290-0.10a+434=652\implies 0.04a-0.10a+724=652 \\\\\\ 0.04a-0.10a=-72\implies -0.06a=-72 \\\\\\ a=\cfrac{-72}{-0.06}\implies {\Large \begin{array}{llll} a=1200 \end{array}} \hspace{5em} \stackrel{6000-3100-1200}{{\Large \begin{array}{llll} b=1700 \end{array}}}\)

Answer:

$20.50

Step-by-step explanation:

The pizza itself is $18. If you wanted 5 toppings you would do .50 multiplied by 5. That would give you a total of $2.50 for the 5 toppings. 18 plus 2.50 is 20.50.

Answer:

A large pizza with 5 toppings will be $20.50

A small pizza with 5 toppings will be $14.50

5 toppings would cost $2.50

Step-by-step explanation:

.50x5=2.50

18.00x2.50=20.50

12.00+2.50=14.50

I hoped this helped

Answer:

0, 10, 8, 2

Step-by-step explanation:

Answer:

0 10 8 2

Step-by-step explanation:

edg 2021

Answer:

  ∠B ≈ 50.9°

Step-by-step explanation:

The area formula for a triangle can be used to find the missing angle.

We don't want confusion between A for area and angle A, so we define Q as the area of the triangle with sides a, c, and included angle B. In this scenario, 'a' represents side BC (opposite angle A), and 'c' represents side AB (opposite angle C).

  Q = (1/2)ac·sin(B)

Solving for B, we have ...

  2Q/(ac) = sin(B)

  B = arcsin(2Q/(ac)

  B = arcsin(2(64)/(11(15)) = arcsin(128/165)

  ∠B ≈ 50.9°

Answer:

It is (B) ED2021

Explanatory variable: time spent streaming videos

Response variable: time spent exercising

Answer:

a of a is a

Step-by-step explanation:

a²% not sure of the answer

The expression of logarithmic function, f(x) = ln (1/gᵏ) after all possible expansion is equals to the f(x) = - k × ln( g).

In mathematics, the logarithmic function is defined as inverse function to exponent function and defined as f(x) = logₐx where a is base of function. Properties of Logarithmic Functions :

We have, a natural logarithmic function, i.e., base = 10, f(x) = ln (1/gᵏ) and we have to expand it. To expand logarithms means write them as a sum or difference product of logarithms. The order to apply rules is quotient rule, product rule and then power rule. So, f(x) = ln (1/gᵏ)

applying quotient rule,

=> f(x) = ln(1) - ln( gᵏ)

Appling power rule,

=> f(x) = ln(1) - k ln( g)

Applying Zero Exponent Rule,

=> f(x) = 0 - k × ln( g)

Hence, the required expansion is f(x) = - k × ln( g).

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Answer:

C= -5t+30

The slope of the function is -5 which reveals the number of chocolates Natalie eats each night.

Step-by-step explanation:

The function to calculate her regular pay rate is y = 55x  + 75.

Her regular pay rate is 12 dollars.

Juliana expects to work overtime this week. She will work 40 hours at her regular pay rate.

She usually work 15 hours at 5 dollars per hour more than her regular rate.

Therefore, the function to calculate how much money she will make base on her regular pay rate is as follows:

let her regular pay rate = x

Therefore,

y = 40x + 15(x + 5)

y = 55x  + 75

Let's find her regular pay rate when she earns 735 dollars(including the overtime)

Therefore,

735 = 40x + 15(x + 5)

735 = 40x + 15x + 75

735 - 75 = 55x

660 = 55x

x = 660 / 55

x = 12

Therefore, her regular pay rate is 12 dollars.

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For the values like (0.-4) and (1,3.5),the function is h(x)=9x-4.

Given a table which contain values of the function h(x) and the respective values of x.

We are required to form the function.

Function is basically the relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain and the values that we get from the function is known as part of range of the function.

We have to just take two points like (0.-4) and (1,3.5).

We have to just form the equation.

y-(-4)={5-(-4)}/{1-0}(x-0)

y+4=9x

y=9x-4

h(x)=9x-4

Hence for the values like (0.-4) and (1,3.5),the function is h(x)=9x-4.

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Question is incomplete as it should include the attached figure.

Graph for the modulus function is as follows.

What is modulus function?

A modulus function is a function that determines a number or variable's absolute value.

Main body:

Given that,

Which graph represents the function f(x) = 4⌈x⌉?

Now,

to represent the graph of Y =  IxI-4 .

So,

Taking x = 0, we get

Y =  IxI -4

Y =  I0I -4

Y = -4

Taking x = 1, we get

Y =  IxI - 4

Y =  I1I -4

Y = -3

Taking x = 2, we get

Y =  IxI - 4

Y =  I2I - 4

Y = -2.

Taking x = -1, we get

Y =  IxI - 4

Y =  I-1I - 4

Y = 1 -4

Y = -3

Taking x = -2, we get

Y =  IxI - 4

Y =  I-2I - 4

Y = -2

Hence the graph for the function is as follows.

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The probability that 3 boys are selected for the relay team given that the first election was a girl is approximately 0.122, or 12.2%.

Let B represent the decision to select three boys for the relay team whereas A represents the scenario when a girl was chosen first.

P(B|A) is the conditional probability of B given A.

The Bayes theorem gives us:

P(B|A) is equal to P(A|B)*P(B)/P(A).

Given that the relay team consists of 3 boys, the probability that a girl would be chosen as the first team member is P(A|B). Therefore:

P(A|B) = 7/13 * 6/12 * 5/11 * 7/10 = 0.0871

P(B) represents the likelihood of choosing three males for the relay team in an arbitrary manner.

P(B) = (7C3 * 7C1) / (14C4) = 35/143

P(A) represents the likelihood that a girl will be chosen as the first team member without any restrictions.

P(A) = 7/14 = 1/2

Combining everything, we get the following: P(B|A) = P(A|B) * P(B) / P(A) = 0.0871 * 35/143 / (1/2) = 0.1220.122, or 12.2%.

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The angle 7 is the alternative interior angle to angle 2.

Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.

They are the angles that are on opposite sides of the transversal and inside the two parallel lines.

Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.

We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.

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Answer:

The numbers are 25 and 26.

Step-by-step explanation:

When you multiply 25 with 26 you get their product, 650. And when you add them you get the answer 51.

Using the z-distribution, as we are working with a proportion, it is found that the 75% confidence interval for the population mean of people that spend over 20 hours per week on their phones is given by:

CI = (74.36%, 75.64%).

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, the parameters are:

\(n = 6000, \pi = \frac{4500}{6000} = 0.75, z = 1.15\)

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.15\sqrt{\frac{0.75(0.25)}{6000}} = 0.7436\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.15\sqrt{\frac{0.75(0.25)}{6000}} = 0.7564\)

Using percentages, the interval is given by:

CI = (74.36%, 75.64%).

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Answer:

x-7

Step-by-step explanation:

1. Find the GCF of x^2-7x (which is x) and factor x^2-4x-21

2. Multiply 1/(x-7)(x+) by x and 4/x(x-7) by (x+3) to get (x-7) as both denominators

The least common denominator of the expression is x - 7

The expression is given as:

\(\frac{4}{x^2 - 7x} + \frac{1}{x^2 - 4x - 21}\)

Expand the expressions

\(\frac{4}{x(x - 7)} + \frac{1}{(x + 3)(x - 7)}\)

Bring the common term of both denominators

Common term = x - 7

Hence, the least common denominator is x - 7

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Answer:

DISCLAIMER:I'M NOT REALLY GOOD AT MATH

Surface area=¶r squared.

¶=3.14

Radius=D/2

=10/2

5

therefore,3.14×5×5

=78.5

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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Answer:

7w=63

63÷7=9

so, (w=9)

Answer:

9

Step-by-step explanation:

3*9 = 27 4*9=36

36 + 27 = 63

Answer:

B

Step-by-step explanation:

f^-1(x)=3x/7-9/7

1. If you rented the jet ski for 9 RTUs, it would cost $90 USD.

2. If we paid $80 USD for the jet ski rental, the rental time would be 8 RTUs.

3. If you rented the jet ski for 2.5 RTUs, it would cost $25 USD.

We are given that 1 unit of 1 = 1 RTU = $10.

Then, 9 RTUs will cost:

= 9 * $10

= $90

To calculate how long was the rental in RTU, you can divide the total cost by the cost of each unit which is:

= $80 / $10

= 8 RTUs

2 units of 1 = 2 RTUs = $20

1 unit of 0.5 = 0.5 RTUs = $5

So, the total cost of jet ski for 2.5 RTU will be:

= $20 + $5

= $25

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