A runner, training for a competition, ran on a track every day for 10 weeks. The first week he ran 8 kilometers each day of the week. The second week he increased his daily run by one lap (400 meters). The third week he increased again his daily run by one lap and so on. What is total distance he ran in 10 weeks?

Answer:

domain = real numbers, range = positive real numbers

Step-by-step explanation:

f(x) = a^x

Domain is the set of all real numbers whose values are defined.

Here x is the exponent. There is no restriction for x

So x  can take any value. x  can be positive or negative

Hence, domain is all real numbers.

For range we consider the value of f(x)

For positive x  values , f(x) will be positive

For negative x  values , f(x) will be positive

so , range is positive real numbers

Step 1.

Calculate measure of angle α:

[tex]47^o-38^o=9^o[/tex]

Step 2.

Calculate what fraction of the angle 360° ​​is the angle α:

[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]

Step 3.

Calculate the circumference of the Earth (circle):

[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]

Step 4.

The length of arc is equal 1/40 of the circumference:

[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]

[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]

The distance between Seattle, WA, and San Francisco, CA, calculated using their latitudinal difference on a sphere with a radius of 4000 miles, is approximately 628 miles.

The question is asking for the distance between Seattle, WA and San Francisco, CA based on their respective latitudes and assuming they are on the same longitudinal line. To find the arc length and thus the distance between the two cities, you can use the formula for arc length on a sphere: [tex]\(Arc \ length = (\Delta Latitude \times \pi/180) \times \ Radius \ of\ Earth\)[/tex]. Here, [tex](\Delta Latitude\)[/tex] is the difference in latitude between the cities, which is [tex]\(47^\circ - 38^\circ = 9^\circ\)[/tex]. The radius of Earth is given as 4000 miles. Plugging these values into the formula, you get:

[tex]\(Arc \ length = (9 \times \pi/180) \times 4000\)[/tex]

[tex]\(Arc \ length = (9 \times 3.14/180) \times 4000\)\\\(Arc \ length = (0.157) \times 4000\)\\\(Arc \ length = 628 \ miles\)[/tex]

Therefore, the distance between Seattle and San Francisco, based on latitude and assuming they are directly north and south of each other, is approximately 628 miles.

Answer:

D. 110 deg

Step-by-step explanation:

Angle YVZ and WVX are vertical angles.

A theorem states that vertical angles are congruent.

Angle YVZ is congruent to angle WVX.

m<YVZ = m<WVX = 110 deg

Answer:

110 degrees

Step-by-step explanation:

<YVZ is vertically opposite to a known angle <WVX

Vertically Opposite Angles are equal

<YVZ = WVX

<WVX = 110 degrees.                Given

Therefore YVZ = 110 degrees.  Property of Vertically opposite angles

Answer:

8

Step-by-step explanation:

We will use the math operation division to find the answer. Division takes a total and divides it into equal amounts. We have a total of 96 and need equal amounts in to each of the 12 groups.

96/12=8 students per group

Answer:15 dollar a month movie offer is

Answer:

$125

Step-by-step explanation:

original cost - discount = discounted price

discount = original cost * .2

original cost - original cost *.2 = 100

Factor out the original cost

original cost ( 1-.2) = 100

original cost *.8 = 100

Divide each side by .8

original cost *.8/.8 = 100/.8

original cost = 125

Answer:

mean: 27

median: 25

mode: 25

Step-by-step explanation:

Mean: 297/11 =27

Median: put the values in order; 22,23,24,25,25,25,28,29,31,32,33. the median is 25

Mode: 25

Final answer:

The mean of the data set is 27, the median is 25, the mode is also 25, and the range is 11.

Explanation:

To find the mean, you add up all the numbers and then divide by the number of values. The median is the middle value when the numbers are in order. The mode is the number that appears the most. The range is the difference between the highest and lowest numbers.

First, let's order the data from least to greatest: 22, 23, 24, 25, 25, 25, 28, 29, 31, 32, 33.

Now, we calculate each:

1.The mean is (22 + 23 + 24 + 25 + 25 + 25 + 28 + 29 + 31 + 32 + 33) / 11 which equals 297 / 11 which equals 27.
2.The median is the middle number, which is 25 because there are five numbers on each side of it in the ordered list.

3.The mode is the number that appears most frequently - that's 25, as it appears three times.

4.To find the range, subtract the smallest number from the largest: 33 - 22 equals 11.

Answer:(2x + 9i)(2x - 9i)

Step-by-step explanation:

a^2 - b^2 = (a+b)(a-b)

a^2 + b^2 = (a+bi)(a-bi) = a^2 + abi - abi - b^2 i^2

But -b^2 i^2 = +b^2

Answer:

[tex](4x+9i)(4x-9i)[/tex]

Step-by-step explanation:

Here, we have to apply this complex numbers property:

[tex]a^2 + b^2 = (a+bi)(a-bi)[/tex]

So, the given expression [tex]4x^2+81[/tex], can be rewrite as factor using the property:

[tex]4x^2+81=(4x+9i)(4x-9i)[/tex]

Because, if

[tex]a^2=x^2 \ and \ b^2=81\\\ then \ a=x \ and \ b=9[/tex]  

Therefore, the factors are [tex](4x+9i)(4x-9i)[/tex]

Answer: C. [tex]\frac{7}{25}-\frac{24}{25}i[/tex]

Step-by-step explanation:

1. You have the following division:

[tex]\frac{4-3i}{4+3i}[/tex] (As you can see, to find the conjugate of  4-3i you must change the sign between the terms).

2. To solve this division, you must multiply the numerator and the denominator by the conjugate of the denominator, as following:

[tex]=\frac{(4-3i)}{(4+3i)}\frac{(4-3i)}{(4-3i)}=\frac{16-12i-12i+9i^{2}}{16-9i^{2}}[/tex]

3. Keeping on mind that [tex]i^{2}=-1[/tex], you have:

[tex]=\frac{16-12i-12i+9(-1)}{16-9(-1)}[/tex]

4. Simplifying:

[tex]=\frac{7-24i}{25}=\frac{7}{25}-\frac{24}{25}i[/tex]

5. The result is:

[tex]\frac{7}{25}-\frac{24}{25}i[/tex]

The quotient of the complex number 4 - 3i divided by its conjugate is  [tex]\dfrac{7}{25} -\dfrac{24}{25}i[/tex]. And option (C) is correct.

Given data:

The complex number is, 4 - 3i.

To find: The quotient when divided by conjugate of given complex number.

For a given complex number say, a + bi, the conjugate is given as,

a - bi

Then, the conjugate of the given complex number is, 4 + 3i.

Divide the given complex number with its conjugate as,

[tex]=\dfrac{ 4 - 3i}{4 + 3i}\\\\=\dfrac{ 4 - 3i}{4 + 3i} \times \dfrac{4-3i}{4-3i} \\\\=\dfrac{(4-3i)^{2}}{4^{2}-(3i)^{2}}[/tex]

Since, [tex]i^{2} =-1[/tex].

Solving further as,

[tex]=\dfrac{4^{2}+(3i)^{2}-2(4)(3i)}{16-9(-1)} \\\\=\dfrac{16+9(-1)-24)}{25}} \\\\=\dfrac{7}{25} -\dfrac{24}{25}i[/tex]

Thus, we can conclude that the quotient of the complex number 4 - 3i divided by its conjugate is  [tex]\dfrac{7}{25} -\dfrac{24}{25}i[/tex]. And option (C) is correct.

Learn more about the conjugate of complex number here:

https://brainly.com/question/18392150

Answer: C

Step-by-step explanation:

[tex]\dfrac{x+2}{15} =\dfrac{x+1}{5}[/tex]

cross multiply: 5(x + 2) = 15(x + 1)

distribute: 5x + 10 = 15x + 15

                -5x          -5x          

                          10 = 10x + 15

                        -15           -15

                          -5  = 10x

                           [tex]\dfrac{-5}{10}=\dfrac{10x}{10}[/tex]

                           [tex]-\dfrac{1}{2} =x[/tex]

Final answer:

The height of the new cones will be 16.5 inches.

Explanation:

To find the height of the new cones, we can use the formula for the volume of a cone:

V = (1/3)πr^2h

Let's denote the radius of the new cones as r2 and the height of the new cones as h2. We know that the volume of the new cones will be the same as the volume of the existing cones:

(1/3)π(r2)^2h2 = (1/3)π(r1)^2h1

Substituting the given values, r1 = 22 inches (radius of existing cones) and h1 = 66 inches (height of existing cones), we can solve for h2:

(1/3)π(44)^2h2 = (1/3)π(22)^2(66)

Dividing both sides by (1/3)π(44)^2, we get:

h2 = h1(r1/r2)^2

Plugging in the values, h1 = 66 inches and r1 = 22 inches, and r2 = 44 inches, we can calculate:

h2 = 66(22/44)^2

h2 = 66(1/2)^2

h2 = 66(1/4)

h2 = 66/4

h2 = 16.5 inches

Answer:

33%

Step-by-step explanation:

The area of the entire circle:

The radius is 4+3+3 = 10

Area of a circle= pi * r^2

Area of largest circle      = pi * 10^2 = 100 pi

Area of blue ring = Area of blue circle - area of inner white circle

The blue circle has a radius of (4+3) = 7

The inner white circle had a radius of 4

Substituting what we know

Area of blue ring = Area of blue circle - area of inner white circle

                               = pi * r^2 - pi*r^2

                               = pi * 7^2 - pi *4^2

                                = 49pi - 16pi

                                = 33 pi

The percentage of the logo that is blue is the blue ring/ area of largest circle

percentage = 33 pi/100 pi

Canceling pi

percentage = 33/100

                    = 33 %

Answer:

Employers offer bonuses ,health insurances, medical facilities ,residence facilities and other facilities  to their full time employees.

Step-by-step explanation:

Employees play a vital role in progress of an organization.

they need inspiration to work better and to make company's rank better.

and for their inspiration and to enhance the relationship with employees, employers offer them bonuses,health insurances, medical facilities ,residence facilities and other facilities

Answer:

The common benefits of getting a full-time job are:

Remember that a full-time job has to have 40 hours per week. So, to compensate this amount of time spent in the company, they tend to "protect" their employees with better health insurance, their Social Security will give credits, which apply to retirement, and in case of accidents, their insurance will cover all costs.

All these variables make these jobs attractive in order to make people work even more.

Answer:

She will use 13 quarter cups of oatmeal

Step-by-step explanation:

3 1/4 = 13/4

x/4 = 13/4

4(x/4) = 4(13/4)

x = 13

About Slope - Intercept Form:

About Standard Form:

About Point - Slope Form:

Other Info:

Hope this information helps!!! :)

A recursive rule for a geometric sequence:

[tex]a_1\\a_n=r\cdot a_{n-1}[/tex]

[tex]a_1=1,\ a_2=3,\ a_3=9,\ a_4=27\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\to r=\dfrac{3}{1}=\dfrac{9}{3}=\dfrac{27}{9}=3\\\\\boxed{a_1=1,\qquad a_n=3\cdot a_{n-1}}[/tex]

Answer:

a. [tex]y=830*(0.87)^x[/tex]

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: [tex]y=a*b^x[/tex], where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

[tex]13\%=\frac{13}{100}=0.13[/tex]

Upon substituting our given values in exponential decay function we will get

[tex]y=830*(1-0.13)^x[/tex]

[tex]y=830*(0.87)^x[/tex]

Therefore, the exponential model [tex]y=830*(0.87)^x[/tex] represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

[tex]y=830*(0.87)^2[/tex]

[tex]y=830*0.7569[/tex]

[tex]y=628.227\approx 628.23[/tex]

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be [tex]\frac{830}{2}=415[/tex].

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

[tex]415=830*(0.87)^x[/tex]

Upon dividing both sides of our equation by 830 we will get,

[tex]\frac{415}{830}=\frac{830*(0.87)^x}{830}[/tex]

[tex]0.5=0.87^x[/tex]

Let us take natural log of both sides of our equation.

[tex]ln(0.5)=ln(0.87^x)[/tex]

Using natural log property [tex]ln(a^b)=b*ln(a)[/tex] we will get,

[tex]ln(0.5)=x*ln(0.87)[/tex]

[tex]\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}[/tex]

[tex]\frac{ln(0.5)}{ln(0.87)}=x[/tex]

[tex]\frac{-0.6931471805599}{-0.139262067}=x[/tex]

[tex]x=4.977286\approx 4.98[/tex]

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

To find when a stereo system purchased for $830 and depreciating at 13% per year will be worth half of its value, use the exponential decay formula V(t) = [tex]P * (1 - r)^t[/tex]. After 2 years, the stereo is worth approximately $627.77, and it will be worth half its original value after about 5.42 years.

An exponential decay model can represent the value of an asset decreasing over time. For a stereo system purchased for $830 with a yearly depreciation of 13%, the model takes on the form of V(t) = [tex]P * (1 - r)^t[/tex], where:

V(t) is the value of the stereo system after t years.

P is the initial purchase price, which is $830.

r is the rate of decay per year, which is 13% or 0.13.

t is the number of years since the purchase.

The value of the stereo system after 2 years can be calculated using the above model:
[tex]V(2) = 830 * (1 - 0.13)^2 = 830 * 0.87^2[/tex]
= 830 * 0.7569
= $627.77 approximately.

To find when the stereo will be worth half the original value, we set [tex]V(t) = rac{P}{2}[/tex] and solve for t:

415 = [tex]830 * (1 - 0.13)^t[/tex]
[tex]0.5 = (1 - 0.13)^t[/tex]
[tex]Log_0.87(0.5) = t[/tex]
t
t = 5.42

The stereo will be worth half its original value after approximately 5.42 years.

Answer:

[tex]\text{d.}\quad a_n=-2.25(2)^{n-1}[/tex]

Step-by-step explanation:

The common ratio is given as 2, so the base of any exponential must be 2 (not -2 or 2.25). The 4th term is negative, so the initial value must be negative (since the multiplying factor is positive). The only selection matching these requirements is d.

You know the general term is ...

... an = a1·r^(n-1)

so the 4th term is

... -18 = a1·2^(4-1) = 8·a1

Then the first term is ...

... a1 = -18/8 = -2.25 . . . . . confirms our choice of answer d.

Answer:

$356.48

Step-by-step explanation:

We have been given that a jewelry salesperson earns [tex]6\frac{2}{5}[/tex]% commission on all sales. Today she sold $5,570 in jewelry.

To find the total commission earned by salesperson is same as finding the [tex]6\frac{2}{5}[/tex]% of 5,570.  

Let us convert [tex]6\frac{2}{5}[/tex] in decimal form.  

[tex]6\frac{2}{5}=6.4[/tex]

[tex]\text{Total commission earned by salesperson}=\frac{6.4}{100}\times 5,570[/tex]

[tex]\text{Total commission earned by salesperson}=0.064\times 5,570[/tex]

[tex]\text{Total commission earned by salesperson}=356.48[/tex]

Therefore, the total commission earned by salesperson is $356.48.

Bryan's next step should look like: [tex]\[37.3 - 5.2\][/tex].

To evaluate the given expression, Bryan should follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).

Start with what's inside the parentheses:

[tex]\(42 / 3.2 = 13.125\)[/tex], and [tex]\(10(0.2) = 2\)[/tex]. So, inside the parentheses, we have: [tex]\(16 - 2 + 3 = 17\)[/tex].

Multiply and divide from left to right:

[tex]\(2.5 \times 17 = 42.5\).[/tex]

Substitute back into the expression:

[tex]\(42.5 - 5.2\).[/tex]

Complete the subtraction:

[tex]\(42.5 - 5.2 = 37.3\).[/tex]

Therefore, Bryan's next step should look like:

[tex]\[37.3 - 5.2\][/tex]

After this step, Bryan would perform the subtraction to find the final result. Following PEMDAS ensures that each operation is carried out correctly, leading to the accurate evaluation of the expression.

Answer:

0.34

Step-by-step explanation:

I just used a calculator

Answer:

Value of h(2y+6) = -18y -57

Step-by-step explanation:

Given the function rule:

h(u) = -9u -3                               ......[1]

To find h(2y+6)

Substitute u = 2y + 6 in [1] we get;

h(2y+6) = -9(2y+6) - 3

Using distributive property: [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]

h(2y+6) = - 18y - 54 - 3 = -18y - 57

Therefore, the value of [tex]h(2y+6) = -18y - 57[/tex]

Answer:

[tex]x=3.5,y=24[/tex]

Step-by-step explanation:

The smaller triangle joining the midpoints of the bigger right angle triangle will also be a right angle triangle.

Midpoint Theorem-

According to this, the segment joining two sides of a triangle at the midpoints is half the length of the third side.

Applying this,

[tex]\Rightarrow x=\dfrac{1}{2}(4x-7)[/tex]

[tex]\Rightarrow 2x=4x-7[/tex]

[tex]\Rightarrow 4x-2x=7[/tex]

[tex]\Rightarrow 2x=7[/tex]

[tex]\Rightarrow x=\dfrac{7}{2}=3.5[/tex]

So, the hypotenuses of the bigger triangle will be,

[tex]=6(3.5)+4=25[/tex]

Applying the mid point theorem, the hypotenuses of the smaller triangle will be,

[tex]=\dfrac{1}{2}\times 25=12.5[/tex]

Applying Pythagoras theorem in the smaller triangle, the leg will be

[tex]=\sqrt{12.5^2-3.5^2}\\\\=\sqrt{156.25-12.25}\\\\=\sqrt{144}\\\\=12[/tex]

Again applying mid point theorem,

[tex]\Rightarrow y=2\times 12=24[/tex]

Answer:

[tex]g(x)=x^2+7 x+12[/tex]

Step-by-step explanation:

since f(x)=[tex]x^{2}+3 x+2[/tex]

now we are given that this function f(X) is shifted 2 units to the left and we get a function g(x) this means

g(x)=f(x+2) since f(x+2) will shift the function f(x) 2 units to the left.

[tex]g(x)=(x+2)^{2}+3(x+2)+12[/tex]

g(x)=[tex]x^2+4+4 x+3 x+6+2[/tex]

hence, the function g(x)=[tex]x^2+7 x+12[/tex]

Answer:

Option A is correct.

Value of [tex]S_{22} = 15.4[/tex]

Step-by-step explanation:

Given: [tex]a_{12} = 2.4[/tex] and common difference(d) = 3.4

A sequence of numbers is arithmetic i.e,  it increases or decreases by a constant amount each term.

The sum of the nth term of a arithmetic sequence is given by;

[tex]S_n =\frac{n}{2}(2a+(n-1)d)[/tex], where n is the number of terms, a is the first term and d is the common difference.

We also know the nth tern sequence formula which is given by ;

[tex]a_n = a+(n-1)d[/tex]                             ......[2]

First find a.

it is given that [tex]a_{12} = 2.4[/tex]

Put n =12 and d=3.4 in equation [2] we have;

[tex]a_{12} = a+(12-1)(3.4)[/tex]

[tex]a_{12} = a+(11)(3.4)[/tex]

2.4 = a + 37.4

Simplify:

a = - 35

Now, to calculate [tex]S_{22}[/tex]

we use equation [1];

here, n =2 , a =-35 and d=3.4

[tex]S_{22} = \frac{22}{2}(2(-35)+(22-1)(3.4))[/tex]

[tex]S_{22} = (11)(-70+21(3.4))[/tex]

[tex]S_{22} = (11)(-70+71.4)[/tex]

[tex]S_{22} = (11)(1.4)[/tex]

Simplify:

[tex]S_{22} = 15.4[/tex]

Therefore, the sum of sequence of 22nd term i.e, [tex]S_{22} = 15.4[/tex]

Answer:

A. 15.4

Step-by-step explanation:

Answer:

21.76 Centimeters

Step-by-step explanation:

Length - 3.2 Cm

Width - 6.8 Cm

Area = Width * Length (Or other way around)

Multiply:

3.2 * 6.8

= 21.76

- I.A -

So to find the number of solutions this quadratic equation has without actually solving the equation, we are going to be using the discriminant formula. Plug in the numbers and solve:

[tex]D=5^2-4*1*7\\D=25-28\\D=-3[/tex]

Now, here are the rules with discriminants:

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

Answer:

0 real solutions in this equation.