Paula invests $600 at a rate of r% per year simple interest. At the end of 10 years, the total interest earned is $90. Find the value of r.

Answer: R=8

Step-by-step explanation:

-7 is added to 1 making it R= 1+7 resulting in R=8

Answer:

[tex]\huge \boxed{R=8}[/tex]

Step-by-step explanation:

[tex]R-7=1[/tex]

Adding 7 to both sides of the equation.

[tex]R-7+7=1+7[/tex]

[tex]R=8[/tex]

[tex] \LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}[/tex]

We have, Discriminant formula for finding roots:

[tex] \large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}[/tex]

Here,

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

[tex] \large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}[/tex]

[tex] \large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}[/tex]

So here,

[tex]\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}[/tex]

❒ p(x) = x^2 + 2x + 1 = 0

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}[/tex]

So here,

[tex]\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}[/tex]

❒ p(x) = x^2 - x - 20 = 0

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}[/tex]

So here,

[tex]\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}[/tex]

❒ p(x) = x^2 - 3x - 4 = 0

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}[/tex]

[tex]\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}[/tex]

So here,

[tex]\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}[/tex]

━━━━━━━━━━━━━━━━━━━━

Step-by-step explanation:

a)

given: a = 1, b = 5, c = 6

1) Discriminant → ∆= b² − (4*a*c)

∆= b² - (4*a*c)

∆= 5² - (4*1*6)

∆=25 - ( 24 )

∆= 25 - 24

∆= 1

2)

Solve x = (- b ± √Δ ) / 2a

x = ( 5 ± √25 ) / 2*1

x = ( 2 ± 5 ) / 2

x = ( 2 + 5 ) / 2 or x = ( 2 - 5 ) / 2

x = ( 7 ) / 2 or x = ( - 3 ) / 2

x = 3.5 or x = -1.5

b)

given: a = 1, b = 2, c = 1

1) Discriminant → ∆= b² − (4*a*c)

∆= b² - (4*a*c)

∆= 2² - (4*1*1)

∆= 4 - (4)

∆= 4 - 4

∆= 0

2)

Solve x = (- b ± √Δ ) / 2a

x = ( -2 ± √0) / 2*1

x = ( 2 ± 0 ) / 2

x = ( 2 + 0) / 2 or x = ( 2 - 0 ) / 2

x = ( 2 ) / 2 or x = ( 2 ) / 2

x = 1 or x = 1

x = 1 (only one solution)

c)

given: a = 1, b = -1, c = -20

1) Discriminant → ∆= b² − (4*a*c)

∆= b² - (4*a*c)

∆= -1² - (4*1*-20)

∆= 1 - ( -80 )

∆= 1 + 80

∆= 81

2)

Solve x = (- b ± √Δ ) / 2a

x = ( 2 ± √81 ) / 2*1

x = ( 2 ± 9 ) / 2

x = ( 2 + 9 ) / 2 or x = ( 2 - 9 ) / 2

x = ( 11 ) / 2 or x = ( - 7 ) / 2

x = 5.5 or x = -3.5

d)

given: a = 1, b = -3, c = -4

1) Discriminant → ∆= b² − (4*a*c)

∆= b² - (4*a*c)

∆= -3² - (4*1*-4)

∆= 9 - ( -16)

∆= 9 + 16

∆= 25

2)

Solve x = (- b ± √Δ ) / 2a

x = ( 3 ± √25 ) / 2*1

x = ( 3 ± 5 ) / 2

x = ( 3 + 5 ) / 2 or x = ( 3 - 5 ) / 2

x = ( 8 ) / 2 or x = ( - 2 ) / 2

x = 4 or x = -1

Answer:

Step-by-step explanation:

[tex]8(x + 5) = \\ 8(x) + 8(5) \\ = 8x + 40[/tex]

[tex] - 2(3m + 9) \\ = - 2(3m) - 2(9) \\ = - 6m - 18[/tex]

Answer:

3x³ - 14x² - 7x + d = (x + 1)(ax² + bx + c)

--------------------------

  (x + 1)(ax² + bx + c)  

= ax³ + bx² + cx + ax² + bx + c

= ax³ + (a + b)x² + (b + c)x + c

--------------------------

ax³ + (a + b)x² + (b + c)x + c = 3x³ - 14x² - 7x + d

=> a = 3

    a + b = -14

    b + c = -7

    c = d

=> a = 3, b = -17, c = 10, d = 10

Answer:

Scale factor 2.

Step-by-step explanation:

The vertices of shape I are (2,1), (3,1), (4,3), (3,3), (3,2), (2,2), (2,3), (1,3).

The vertices of shape II are (-4,-2), (-6,-2), (-8,-6), (-6,-6), (-6,-4), (-4,-4), (-4,-6), (-2,-6).

Consider shape I is similar to shape II. The sequence that maps shape I onto shape II is a 180 degree clockwise rotation about the origin, and then a dilation by a scale factor of k.

Rule of 180 degree clockwise rotation about the origin:

[tex](x,y)\rightarrow (-x,-y)[/tex]

The vertices of shape I after rotation are (-2,-1), (-3,-1), (-4,-3), (-3,-3), (-3,-2), (-2,-2), (-2,-3), (-1,-3).

Rule of dilation by a scale factor of k.

[tex](x,y)\rightarrow (kx,ky)[/tex]

So,

[tex](-2,-1)\rightarrow (k(-2),k(-1))=(-2k,-k)[/tex]

We know that, the image of (-2,-1) after dilation is (-4,-2). So,

[tex](-2k,-k)=(-4,-2)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]k=2[/tex]

Therefore, the scale factor is 2.

Answer:

180 clockwise rotation about the orgin, 2

Step-by-step explanation:

Answer:

10r²

Step-by-step explanation:

The following data were obtained from the question:

Radius (r) = 5r

Length of arc (L) = 4r

Area of sector (A) =?

Next, we shall determine the angle θ sustained at the centre.

Recall:

Length of arc (L) = θ/360 × 2πr

With the above formula, we shall determine the angle θ sustained at the centre as follow:

Radius (r) = 5r

Length of arc (L) = 4r

Angle at the centre θ =?

L= θ/360 × 2πr

4r = θ/360 × 2π × 5r

4r = (θ × 10πr)/360

Cross multiply

θ × 10πr = 4r × 360

Divide both side by 10πr

θ = (4r × 360) /10πr

θ = 144/π

Finally, we shall determine the area of the sector as follow:

Angle at the centre θ = 144/π

Radius (r) = 5r

Area of sector (A) =?

Area of sector (A) = θ/360 × πr²

A = (144/π)/360 × π(5r)²

A = 144/360π × π × 25r²

A = 144/360 × 25r²

A = 0.4 × 25r²

A = 10r²

Therefore, the area of the sector is 10r².

the area of the sector in terms of r is [tex]10r^2[/tex]

Given :

From the given diagram , the radius of the circle is 5r  and length of arc AB is 4r

Lets find out the central angle using length of arc formula

length of arc =[tex]\frac{central-angle}{360} \cdot 2\pi r[/tex]

r=5r  and length = 4r

[tex]4r=\frac{central-angle}{360} \cdot 2\pi (5r)\\4r \cdot 360=central-angle \cdot 2\pi (5r)\\\\\\\frac{4r \cdot 360}{10\pi r} =angle\\angle =\frac{4\cdot 36}{\pi } \\angle =\frac{144}{\pi }[/tex]

Now we replace this angle in area of sector formula

Area of sector =[tex]\frac{angle}{360} \cdot \pi r^2\\[/tex]

[tex]Area =\frac{angle}{360} \cdot \pi r^2\\\\Area =\frac{\frac{144}{\pi } }{360} \cdot \pi\cdot 25r^2\\\\Area =\frac{ 144 }{360\pi } \cdot \pi\cdot 25r^2\\\\Area =\frac{ 2 }{5 } \cdot 25r^2\\\\\\Area=10r^2[/tex]

So, the area of the sector in terms of r is [tex]10r^2[/tex]

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Answer:

Solution : (15, - 11)

Step-by-step explanation:

We want to solve this problem using a matrix, so it would be wise to apply Gaussian elimination. Doing so we can start by writing out the matrix of the coefficients, and the solutions ( - 5 and - 2 ) --- ( 1 )

[tex]\begin{bmatrix}-4&-5&|&-5\\ -6&-8&|&-2\end{bmatrix}[/tex]

Now let's begin by canceling the leading coefficient in each row, reaching row echelon form, as we desire --- ( 2 )

Row Echelon Form :

[tex]\begin{pmatrix}1\:&\:\cdots \:&\:b\:\\ 0\:&\ddots \:&\:\vdots \\ 0\:&\:0\:&\:1\end{pmatrix}[/tex]

Step # 1 : Swap the first and second matrix rows,

[tex]\begin{pmatrix}-6&-8&-2\\ -4&-5&-5\end{pmatrix}[/tex]

Step # 2 : Cancel leading coefficient in row 2 through [tex]R_2\:\leftarrow \:R_2-\frac{2}{3}\cdot \:R_1[/tex],

[tex]\begin{pmatrix}-6&-8&-2\\ 0&\frac{1}{3}&-\frac{11}{3}\end{pmatrix}[/tex]

Now we can continue canceling the leading coefficient in each row, and finally reach the following matrix.

[tex]\begin{bmatrix}1&0&|&15\\ 0&1&|&-11\end{bmatrix}[/tex]

As you can see our solution is x = 15, y = - 11 or (15, - 11).

[tex]\frac{x^2}{3}[/tex] is the same as [tex]\frac{1}{3}x^2[/tex]

Dividing by 3 is the same as multiplying by the fraction 1/3

Answer:

Step-by-step explanation:

From  x = -2 to x = 0 function is decreasing, but for x= -1 function doesn't exist, so we need to exclude x = -1 from (-2, 0)

Answer:

4√5

Step-by-step explanation:

√80 = √4·4·5 = √4²·5 = 4√5

The absolute value of any number is never negative. Absolute value represents distance, and negative distance is not possible (it doesn't make any sense to have a negative distance). Specifically, it is the distance from the given number to 0 on the number line.

The result of an absolute value is either 0 or positive.

Examples:

| -22 | = 22

| -1.7 | = 1.7

| 35 | = 35

The vertical bars surrounding the numbers are absolute value bars

Answer:

-1-9i (the second option)

Step-by-step explanation:

(2 – 5i) – (3 + 4i)

=2-5i-3-4i

= -1-9i

-1 – 9i this expression is equal to (2 – 5i) – (3 + 4i).

so, 2nd option is correct.

Here, we have,

To simplify the expression (2 – 5i) – (3 + 4i),

we need to perform the subtraction operation for both the real and imaginary parts separately.

The real part subtraction is done as follows: 2 - 3 = -1.

The imaginary part subtraction is done as follows: -5i - 4i = -9i.

Combining the real and imaginary parts, we get -1 - 9i.

Therefore, the expression (2 – 5i) – (3 + 4i) is equal to -1 - 9i.

Among the given options, the expression that matches this result is O-1 - 9i.

Hence, -1 – 9i this expression is equal to (2 – 5i) – (3 + 4i).

so, 2nd option is correct.

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Answer:

Two expressions for the perimeter would be

22x+23 and 2x+3x+17x+7+16

Step-by-step explanation:

you want to add the variables of the same kind in this case

2x        

3x         7

17x       16

_________

22x  +     23

Complete question is;

A student scores 56 on a geography test and 267 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 22.

If the data for both tests are normally distributed, on which test did the student score better?

Answer:

The geography test is the one in which the student scored better.

Step-by-step explanation:

To solve this question, we will make use if the z-score formula to find the w test in which the student scored better. The z-score formula is;

z = (x - μ)/σ

Now, for geography, we are given;

Test score; x = 56

Mean; μ = 80

Standard deviation; σ = 20

Thus, the z-score here will be;

z = (56 - 80)/20

z = -1.2

Similarly, for Mathematics, we are given;

Test score; x = 267

Mean; μ = 300

Standard deviation; σ = 22

Thus, the z-score here will be;

z = (267 - 300)/22

z = -1.5

Since the z-score for geography is lesser than that of Mathematics, thus, we can conclude that the geography test is the one in which the student scored better.

Answer:

The mean ≈ 90

The median = 95

The mode = 95 & 100

The range = 37

Step-by-step explanation:

We will base out conclusion by calculating the measures of central tendency of the distribution i.e the mean, median, mode and range.

– Mean is the average of the numbers. It is the total sum of the numbers divided by the total number of students.

xbar = Sum Xi/N

Xi is the individual student score

SumXi = 63+66+70+81+81+92+92+93+94+94+95+95+95+96+97+98+98+99+100+100+100

SumXi = 1899

N = 21

xbar = 1899/21

xbar = 90.4

xbar ≈ 90

Hence the mean of the distribution is approximately equal to 90.

– Median is number at the middle of the dataset after rearrangement.

We need to locate the (N+1/2)the value of the dataset.

Given N =21

Median = (21+1)/2

Median = 22/2

Median = 11th

Thus means that the median value falls on the 11th number in the dataset.

Median value = 95.

Note that the data set has already been arranged in ascending order so no need of further rearrangement.

– Mode of the data is the value occurring the most in the data. The value with the highest frequency.

According to the data, it can be seen that the value that occur the most are 95 and 100 (They both occur 3times). Hence the modal value of the dataset are 95 and 100

– Range of the dataset will be the difference between the highest value and the lowest value in the dataset.

Highest score = 100

Lowest score = 63

Range = 100-63

Range = 37

Answer:

Step-by-step explanation:

To solve first take logarithm to both sides

That's

But

So we have

[tex]x = log_{10}(1200) [/tex]

Write 1200 as a number with the factor 100

That's

1200 = 100 × 12

So we have

Using the rules of logarithms

That's

Rewrite the expression

That's

x = 3.079

So we have the final answer as

Hope this helps you

Answer:

cos A = 3/5

Step-by-step explanation:

sin A = 4/5

sin^2 A + cos^2 A = 1

(4/5)^2 + cos^2 A = 1

16/25 + cos^2 A = 1

cos^2 A = 9/25

cos A = 3/5

Answer:

The question is missing the values, I found a possible matching question:

a city has a population of 380,000 people. suppose that each year the population grows by 7.5%. what will be the population after 6 years

Answer:

After 6 years, the population will be 586, 455 people

Step-by-step explanation:

This growth is similar to the growth of an invested amount of money, which is compounded annually, yielding a future value, when it increases by a certain interest rate. Hence the formula for compound interest is used to determine the population after 6 years as follows:

[tex]FV = PV (1+ \frac{r}{n})^({n \times t})[/tex]

where

FV = future value = population after 6 years = ???

PV = present value = current  population = 380,000 people

r = interest rate = growth rate = 7.5% = 7.5/100 = 0.075

n = number of compounding periods per year = annually = 1

t = time of growth = 6 years

[tex]FV = 380,000 (1+ \frac{0.075}{1})^({1 \times 6})\\FV = 380,000 (1.075)^{6}\\FV= 380,000 (1.5433015256)\\FV = 586,454.58\\FV= 586,455\ people[/tex]

Therefore, after 6 years, the population will be 586, 455 people

Step-by-step explanation:

Question no 1 ans is -10.

Question no 2 ans is 14.

Question no 3 ans is 7.

Question no 4 ans is 14.

Answer:

Below

Step-by-step explanation:

● y -(-3) = (1/4) (x-9)

Replace 1/4 by 0.25 to make it easier

● y + 3 = 0.25(x-9)

● y + 3 = 0.25x - 2.25

Add 3 to both sides

● y +3-3 = 0.25x -2.25-3

● y = 0.25x -5.25

To the coordinates of a point from this line replace x by a value.

The easiest one is 0.

● y = 0.25×0 -5.25

● y = 5.25

5.25 is 21/4

So the coordinates are (0, 21/4)

The coordinate of a point on the line whose equation in point-slope form is y − (−3) = 1/4 (x − 9) is (9, -3)

The equation of a line in point-slope form is expressed as;

[tex](y-y_0)=m(x-x_0)[/tex] where:

m is the slope

[tex](x_0, y_0)[/tex] is the point on the line.

Given the equation in the point-slope form expressed as

[tex]y - (-3) = 1/4 (x - 9)[/tex]

Comparing the general equation with the given equation:

[tex]y_0 = -3\\x_0 = 9[/tex]

Hence the coordinate of a point on the line whose equation in point-slope form is y − (−3) = 1/4 (x − 9) is (9, -3)

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Hey there! I'm happy to help!

A mixed number is a whole number and a fraction. We already see that our whole number is 7.

Our decimal is 0.13. Since this goes into the hundredths place, we can rewrite this as 13/100. This cannot be simplified anymore.

Therefore, 7.13 is 7 13/100 in lowest terms.

Have a wonderful day! :D

Greetings from Brasil...

First, let's make the mixed fraction improper:

- (3 3/8)

- { [(8 · 3) + 3]/8}

- { [24 + 3]/8}

- {27/8}

- (3 3/8) - (7/8)

- (27/8) - (7/8)

as the denominators are equal, we operate only with the numerators

- 34/8      simplifying

Answer:

Step-by-step explanation:

-3 3/8 - 7/8

convert -3 3/8 to improper fractions

_   27   _   7

    8            8

_   27 - 7

       8      

simplify

_   34

     8

convert to proper factions

_   17

     4

-  4 ¹/₄

Answer:

21x + 12

Step-by-step explanation:

In math, it is

21x + 2(6).

so we have

21x + 2(6) = 21x + 12.

Answer:

c. variables, constants, and functions

Step-by-step explanation:

A predicate is the property that some object posses. Predicate calculus is a kind of logic that combines the categorical logic with propositional logic. The formal syntax of a predicate calculus contains 3 Terms which consist  of:

1.  Constants and Variables

2. Connectives

3. Quantifiers

But in arguments to predicates and functions, the terms  can only be combination of variables, constants, and functions.

Answer:

w/2

Step-by-step explanation:

Calculating half of something is the same as dividing it by 2. In this case, the "something" is w so the answer is w/2.

Answer:

757

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sum of 3/8 and -5/12:

Least common denominator of 8 & 12 = 24

[tex]\frac{3}{8}+\frac{-5}{12}=\frac{3*3}{8*3}+\frac{-5*2}{12*2}\\\\\\=\frac{9}{24}+\frac{-10}{24}\\\\\\=\frac{-1}{24}[/tex]

Finding -15/8 * 16/27:

[tex]\frac{-15}{8}*\frac{16}{27}=\frac{-5*2}{1*9}=\frac{-10}{9}[/tex]  

Reciprocal of -10/9 = -9/10

-1/24 ÷ -9/10 = [tex]\frac{-1}{24}*\frac{-10}{9}=\frac{1*5}{12*3}[/tex]

= [tex]\frac{5}{24}[/tex]

Answer:

The intensity of the earthquake in Chile was about 16 times the intensity of the earthquake in Haiti.

Step-by-step explanation:

Given:

magnitude of earthquake in Chile =  8.2

magnitude of earthquake in Haiti = 7.0

To find:

Compare the intensities of the two earthquakes

Solution:

The magnitude R of earthquake is measured by R = log I

R is basically the magnitude on Richter scale

I is the intensity of shock wave

For Chile:

given magnitude R of earthquake in Chile =  8.2

R = log I

8.2 = log I

We know that:

[tex]y = log a_{x}[/tex]  is equivalent to: [tex]x = a^{y}[/tex]  

[tex]R = log I[/tex]

8.2 = log I becomes:

[tex]I = 10^{8.2}[/tex]

So the intensity of the earthquake in Chile:

[tex]I_{Chile} = 10^{8.2}[/tex]

For Haiti:

R = log I

7.0 = log I

We know that:

[tex]y = log a_{x}[/tex]  is equivalent to: [tex]x = a^{y}[/tex]  

[tex]R = log I[/tex]

7.0 = log I becomes:

[tex]I = 10^{7.0}[/tex]

So the intensity of the earthquake in Haiti:

[tex]I_{Haiti} = 10^{7}[/tex]

Compare the two intensities :

[tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]

[tex]= \frac{10^{8.2} }{10^{7} }[/tex]

= [tex]10^{8.2-7.0}[/tex]

= [tex]10^{1.2}[/tex]

= 15.848932

Round to the nearest whole number:

16

Hence former earthquake was 16 times as intense as the latter earthquake.

Another way to compare intensities:

Find the ratio of the intensities i.e. [tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]

[tex]log I_{Chile}[/tex] - [tex]log I_{Haiti}[/tex] = 8.2 - 7.0

[tex]log(\frac{I_{Chile} }{I_{Haiti} } })[/tex] = 1.2

Convert this logarithmic equation to an exponential equation

[tex]log(\frac{I_{Chile} }{I_{Haiti} } })[/tex] = 1.2

[tex]10^{1.2}[/tex] = [tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]

Hence

[tex]\frac{I_{Chile} }{I_{Haiti} } }[/tex]  = 16

Answer:

The intensity of the 2014 earthquake was about 16 times the intensity of the 2010 earthquake

Step-by-step explanation:

Answer:

1177.58 cm³

Step-by-step explanation:

The volume of a sphere is given by V = (4/3)πr³. In this case, if the width (diameter) of the cup is 16.51cm, then the radius is 8.255 cm. So the volume of the cup, if it were a sphere, would be:

V = (4/3) * 3.14 * (8.255)³ ≈ 2355.1557 cm³

But since this is a hemisphere (i.e., half a sphere), we cut that value in half to get the volume of the cup:

2355.1557 / 2 ≈ 1177.58 cm³

Answer:

idk

Step-by-step explanation:

Answer: y=2x+1

Step-by-step explanation:

plug in the points in to the equation to see what you get