Can you please me with the word problem thank you so much

Answer:

The 3 years investment earns more interest

Step-by-step explanation:

Given

Principal, P = $5,000

Required

Determine which earns more interest

When Rate = 1.75% and Year = 2

Interest is as follows;

[tex]I = \frac{PRT}{100}[/tex]

Substitute 1.75 for R, 5000 for P and 2 for T

[tex]I = \frac{5000 * 1.75 * 2}{100}[/tex]

[tex]I = \frac{17500}{100}[/tex]

[tex]I = \$175[/tex]

When Rate = 1.25% and Year = 3

Interest is as follows;

[tex]I = \frac{PRT}{100}[/tex]

Substitute 1.25 for R, 5000 for P and 3 for T

[tex]I = \frac{5000 * 1.25 * 3}{100}[/tex]

[tex]I = \frac{18750}{100}[/tex]

[tex]I = \$187.5[/tex]

Comparing the interest of both investments, the 3 years investment earns more interest

Answer:

144 ways

Step-by-step explanation:

Number of paintings = 7

Renaissance = 4

Baroque = 3

We are hanging from left to right and we will first hang Renaissance painting before baroque painting.

For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24

For baroque we have 3! Ways of doing so. 3x2x1 = 6

We have 4!ways x 3!ways

= (4x3x2x1) * (3x2x1) ways

= 144 ways

Therefore we have 144 ways to hang the painting.

Answer:  4.17 steps

Step-by-step explanation:

Draw a point to use as the center and then sketch 50 units north (up) and 25 units west (left) and 315° which creates a right triangle that has an angle of 360° - 315° = 45°

Use Pythagorean Theorem to find the length of the hypotenuse.

50² + 25² = hypotenuse²   --> hypotenuse = 55.9 units

Since Musah only walked 50 units along the hypotenuse, he is 5.9 units from the center.

Create another right triangle using the remaining 5.9 units as the hypotenuse.  You can use 45°-45°-90° rules OR sin 45° to find the horizontal distance from the center to be 4.17.

see attachment for sketch

Answer:

The choose D. 15/16

Step-by-step explanation:

[tex] 1\frac{1}{4} \times \frac{3}{4} = \frac{15}{16} [/tex]

I hope I helped you^_^

Answer:

Factors are 1,2,3,4,5,6,10,12,15,20,30,60

Step-by-step explanation:

Hope this helps

Factors refers to those numbers which muntiplied that no.here, numbers that muntiply 60 are 1,2,3,4,5,6,10,12,15,20,30,60.

thus these numbers are factors of 60.

Answer:

y=3x

Step-by-step explanation:

-6/-2=3, -3/-1=3, 3/1=3. 6/2=3

[tex]10[/tex] divisions between $389$ and $390$ so each division is $\frac{390-389}{10}=0.1$

A is 8 division from $389$, so, A is $389+8\times 0.1=389.8$

similarly, C is one division behind $389$ so it is $389-1\times 0.1=388.9$

and B is $390.3$

Answer: The triangles are not congruent

==========================================

Explanation:

For triangle DEF, the missing angle D is

D+E+F = 180

D+80+60 = 180

D+140 = 180

D = 180-140

D = 40

While the missing angle K in triangle JKL is

J+K+L = 180

80+K+50 = 180

K+130 = 180

K = 180-130

K = 50

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

The three angles for triangle DEF are

The three angles for triangle JKL are

We don't have all the angles matching up. We need to have the same three numbers (the order doesn't matter) show up for both triangles in order for the triangles to be congruent. This is because congruent triangles have congruent corresponding angles.

The only pair that matches is E = 80 and J = 80, but everything else is different. So there is no way the triangles are congruent.

Notice how triangle JKL has two congruent base angles (K = 50 and L = 50), so this triangle is isosceles. Triangle DEF is not isosceles as we have three different angles, so this triangle is scalene.

Answer:

3 2/15 <b

Step-by-step explanation:

2 3/5 <b-8/15​

Add 8/ 15 to each side

2 3/5 + 8/ 15 <b-8/15​ + 8/15

2 3/5 + 8 /15 <b

Get a common denominator

2 3/5 *3/3 + 8/15

2 9/15 + 8/15 < b

2 17/15 < b

2 + 15/15 + 2 /15 < b

3 2/15 <b

Answer:

B > 3 2/15

Step-by-step explanation:

Answer:

k=8

Step-by-step explanation:

Since y and x are in direct proportions, the equation is

y= kx, where k is a constant.

when y= 33.6, x=4.2,

33.6= k(4.2)

k= 33.6 ÷4.2

k=8

Answer:

k=8

Step-by-step explanation:

Answer:

(2+7) root 3 equals 9 root 3

Answer: The equation is correct.

Step-by-step explanation:

from the expression,

5x + 3( y + 4x² + 3x ) + 2( y - x² ) = 14x + 10x² + 5y

Open brackets with 3 and 2

5x + 3y  + 12x² + 9x  + 2y - 2x²

Now collect like terms

5x + 9x + 12x² - 2x² + 3y + 2y

14x + 10x² + 5y = 14x + 10x² + 5y  (Q.E.D)

TH equation is correct

Answer: A. $16.13

Step-by-step explanation:

Total students = 82+74+96+99 =351

Sum of earnings of 82 seniors  = $26.75  x 82= $2193.5

Sum of earnings of 74 juniors  = $12.25 x 74 = $906.5

Sum of earnings of 96 sophomores  = $15.50  x 96 = $1488

Sum of earnings of 99 freshmen  =  $10.85 x 99 = $1074.15

Total earnings =  $2193.5  + $906.5+  $1488 +$1074.15

= $5662.15

(Total earnings) ÷ (Total students )

= $5662.15÷ 351

= $16.13

The true statements about the function include:

It should be noted that a function is simply used to illustrate the relationship between variables.

In this case, the given function is f(x) = x^1/3.

The intercept is (0, 5). Also, it can be deduced that as x approaches oo, h(x) approaches infinity.

Learn more about functions on:

brainly.com/question/25638609

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Answer:

The area shaded is 95%

Step-by-step explanation:

The total area under the curve is 100 percent

1 standard deviation away from the mean is 68 percent

2 standard deviations away is 95 percent

The area shaded is 95%

The percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.

The 68-95-99.7 rule is also referred to as the empirical rule or the three-sigma rule and it can be defined as a shorthand which is used in statistics to determine the percentage of a population parameter that lie within an interval estimate in a normal distribution curve.

Basically, the 68-95-99.7 rule states that 68%, 95%, and 99.7% of the population parameter lie within one (1), two (2), and three (3) standard deviations of the mean respectively.

This ultimately implies that, the percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.

Read more on 68-95-99.7 rule here: https://brainly.com/question/24768583

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Answer:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14

Step-by-step explanation:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT

We are given the matrices A and B

[tex]A = \left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}2\\1\\2\end{array}\right][/tex]

Multiplying these matrices:

We multiply matrices by taking the first column of the first matrix and the first row of the second matrix

we will multiply all the terms of the first column of the first matrix and multiply them by the terms of the first row of the second matrix, one by one

[tex]AB = \left[\begin{array}{ccc}2(2) + 3(1) + -1(2)\\0(2) + 2(1) + 5(2)\\2(2) + 4(1) + 0(2)\end{array}\right][/tex]

[tex]AB = \left[\begin{array}{ccc}5\\12\\8\end{array}\right][/tex]

9514 1404 393

Explanation:

Two matrices with dimensions (numbers of (rows, columns)) of (a, b) and (c, d) can only be multiplied if the number of columns in the left matrix is equal to the number of rows in the right matrix. That is, b=c. The dimensions of the product matrix will be (a, d).

For row i of the left matrix and column j of the right matrix, element a(i,j) of the product matrix is the dot-product of row i with column j. (The dot-product of two vectors is the sum of the products of corresponding elements.)

__

The example matrices have (row, column) dimensions (3, 3) and (3, 1), so can be multiplied with a result having dimensions (3, 1).

It is useful to refer to an element of a matrix by specifying the row and column in which it resides. An element of matrix 'A' in row 2 and column 3 can be referred to as A(2,3). Often, subscripts are used, as in ...

  [tex]A_{i,j}[/tex]

For matrix C = A·B, the element C(1,1) will be the sum ...

  A(1,1)B(1,1) +A(1,2)B(2,1) +A(1,3)B(3,1)

Calculators, apps, spreadsheets, and web sites are available that will perform this arithmetic for you. It can be a bit tedious to do by hand.

Here the product is ...

  [tex]A\cdot B=\left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right] \cdot\left[\begin{array}{c}2&1&2\end{array}\right] =\left[\begin{array}{c}2(2)+3(1)+(-1)(2)&0(2)+2(1)+5(2)&2(2)+4(1)+0(2)\end{array}\right] \\\\=\left[\begin{array}{c}5&12&8\end{array}\right][/tex]

G(x)=5x+3

[tex]\\ \sf\longmapsto G(2)[/tex]

[tex]\\ \sf\longmapsto 5(2)+3[/tex]

[tex]\\ \sf\longmapsto 10+3[/tex]

[tex]\\ \sf\longmapsto 13[/tex]

Option c is correct

Answer: y=23

Step-by-step explanation:

If Points and A,B and C lines on the same line then they will have the same slopes so since we have the coordinates of  A and B we will use the to write an equation in slope intercept form.

To write it in slope intercept form we will need to find the slope and the y intercept.

To find the slope you will find the change in the y coordinates and divide it by the change in the x coordinates.

Using the coordinates (-1,7) and (2,19)  the y coordinates are 7 and 19 and the x coordinates are -1 and 2.

Slope :  [tex]\frac{7-19}{-1-2} \frac{-12}{-3} = 4[/tex]   In this case the slope is 4 so we will use that to find the y intercept by using point A coordinate.

  The slope intercept formula says that y=mx +b  where me is the slope and b is the y intercept.

 7=4(-1) + b  

7 = -4 + b

+4   +4

 b= 11       The y intercept is 11.

Now we can write the whole equation as y=4x + 11   .

To answer the question now, where we need to find y , we will plot the x coordinate which is 3 into the equation and solve for y.

 y = 4(3) + 11  

y = 12 + 11

 y = 23

Answer:

Sara studies longer by 15 minutes.

Step-by-step explanation:

Let's calculate how long Sebastian studies for. From 3:15 - 4:15, there is 1 hour and from 4:15 to 4:45, there are 30 minutes so Sebastian studies for 1 hour and 30 minutes. Now, let's calculate how long Sara studies for. From 4:30 - 5:30, there is 1 hour, from 5:30 - 6:00, there are 30 minutes and from 6:00 - 6:15, there are 15 minutes so Sara studies for 1 hour 45 minutes. This means that Sara studies longer by 45 - 30 = 15 minutes.

Answer:

56

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)

75 = 1/2 (94+d)

Multiply by 2

75*2 = 94+d

150 = 94+d

Subtract 94 from each side

150-94 = d

56=d

[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]

Answer:

Your answer is here.Enjoy dude

Answer:

12.56 unit²

Step-by-step explanation:

The form of the circle is:

Let's bring the given to the form of a circle as above:

As per the form, we got r² = 2², so the radius of circle is 2 units.

The area of circle:

Answer:

16.67 or 16 2/3

Step-by-step explanation:

so, as BC is a tangent, it means the angle OBC is 90 degrees.

therefore, the angle BOC is 180 - 90 - 30 = 60 degrees.

that means the angle AOB is 180 - 60 = 120 degrees.

the triangle ABO must be an isosceles triangle, as the sides are both the radius of the circle. so, both remaining angles are the same : half of 180 - 120 = 60 = 30 degrees.

and so, we know that ABC is an isosceles triangle, because both "side angles" are equal = 30 degrees.

so, AB = BC.

and we know the circumference of the circle (50) and can calculate the radius

50 = 2×pi×r

25 = pi×r

r = 25/pi ≈ 7.96

now we have multiple ways to calculate AB.

AB = BC = tan(60) × r

or

AB = sqrt(r² + r² - 2×r×r×cos(120))

or ...

the first one might be easiest.

AB = tan(60) × 7.96 ≈ 13.78

oh, I just recognized, we need the arc AB (not the straight line).

even easier.

50 is the full "arc" of the circle for all 360 degrees.

but we only need the part of the angle AOB = 120 degrees.

so, this is then only the 120/360 part of the full circle circumference.

ABarc = 50 × 120/360 = 50 / 3 ≈ 16.67 or 16 2/3

Answer:

169 [tex]cm^{2}[/tex]

Step-by-step explanation:

Surface area (SA) = 2B + PH

                       SA = 2 ([tex]\frac{1}{2}[/tex] x 9 x 6) + (7+7+9) 5

                             = 2 (27) + (23) 5

                             = 54 + 115

                        SA = 169 [tex]cm^{2}[/tex]

Answer: 36 shingles can be placed on the north part of the house.

Step-by-step explanation:

Given: Length of each shingle = [tex]1\dfrac23[/tex] feet = [tex]\dfrac53[/tex] feet.

The north part of the house has a roof line that is 60 feet across.

Then, the number of  shingles can be placed  on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)

[tex]=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36[/tex]

Hence, 36 shingles can be placed on the north part of the house.

Answer:

y=15x+126

Step-by-step explanation:

the slope is

15 because -8-(-9) is 1 and 6-(-9) is 15 and y is over x so slope 15

To find y intercept start from -8,6 and add 15 to the y value every time you add one to the x value

you will add 8 times and you get 126 as the intercept

Answer:

39/250

Step-by-step explanation:

15 3/5 = 78/5 and percent means per 100, so

(78/5)/100 = (78/5)(1/100)

=78/500 = 39/250

Answer:

Time = 1.45152 seconds

Step-by-step explanation:

1 foot = 0.000189 mile

300 ft = 300*0.000189

300 ft = 0.0567 miles

492 ft = 492*0.000189

492 ft = 0.092988 miles

Distance left to be covered by the train

= 0.092988-0.0567

= 0.036288 miles

Speed= 90mph

Time taken = distance/speed

Time taken= 0.036288/90

Time = 4.032*10^-4 hour

Time = 4.032*10^-4*60*60

Time = 1.45152 seconds

Answer:

The 95% confidence interval is  [tex]84.83< \mu < 90.37[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  [tex]n = 113[/tex]

     The sample mean is  [tex]\= x = 87.6[/tex]  

      The standard deviation is  [tex]\sigma = 15[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

            [tex]\alpha = 100 - 95[/tex]

             [tex]\alpha = 5\%[/tex]

             [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value  is  

              [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

              [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma}{ \sqrt{n} }[/tex]

=>          [tex]E = 1.96 * \frac{ 15}{ \sqrt{113} }[/tex]

=>          [tex]E = 2.77[/tex]

The  95% confidence interval is mathematically represented as

          [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

        [tex]87.6 - 2.77< \mu < 87.6 + 2.77[/tex]

        [tex]84.83< \mu < 90.37[/tex]