What is the cross-section of a cone that is perpendicular to the base? Rectangle that is perpendicular to the base? Cylinder that is parallel to the base? Triangular Prism that is parallel to the base? (urgent now please answer)

Answer:

Principal Invested in Municipal Bonds is $16,000

Principal Invested in Corporate Bonds is $15,000

Step-by-step explanation:

If;

Principal Invested in municipal bonds = a

Principal Invested in corporate bonds = b

then we have;

a + b = $31,000 --------------------------------Equation 1

0.075a + 0.085b = $2,475  ---------------Equation 2

From equation 1 we have;

a = 31,000 - b

By putting the values of a in Equation 2 we get;

0.075 (31,000 - b) + 0.085b = 2,475

2,325 - 0.075b + 0.085b = 2,475

0.01b = 150

b = $15,000

By putting the values of b in equation 1 we get;

a = $16,000

Final answer:

Reggie Means invested $16,000 in municipal bonds at 7.5% interest and $15,000 in corporate bonds at 8.5% interest to earn a total annual interest of $2,475.

Explanation:

Let the amount invested in municipal bonds be $x. Thus, the amount invested in corporate bonds will be $(31,000 - x). The municipal bonds earn 7.5% annual interest and the corporate bonds earn 8.5% interest. The total annual interest from both investments is $2,475.

To calculate the interest from municipal bonds, use the formula Interest = Principal × Rate × Time. The interest from municipal bonds is 0.075x (since 7.5% is the same as 0.075).

Similarly, for corporate bonds, the interest will be 0.085(31,000 - x). The sum of these interests equals $2,475:

0.075x + 0.085(31,000 - x) = 2,475

Solving this equation:

Answer:

y=\frac{5}{3}x-5

Step-by-step explanation:

Answer:

7/15

Step-by-step explanation:

11+7+9+3= 30

11= red

3=yellow

11+3=14

=14/30

=7/15

Answer:

7/15

Step-by-step explanation:

Probability of an event is the number of possible outcome divided by the total outcome. It is a ratio. The probability that an event will or will not happen is 1 as those are the only two possibilities.

Given that the flower shop has 11 red roses, 7 pink roses, 9 white he roses , and 3 yellow roses in stock , the total number of flower available

= 11 + 7 + 9 + 3

= 30 flowers

The probability that a rose selected is ;

red = 11/30

yellow = 3/30

the probability they the selected rose is red or yellow

= 11/30 + 3/30

= 14/30

= 7/15

To use the Distributive Property on the expression 8(5 - 1), you would multiply 8 by each term inside the parentheses, simplify, and perform the subtraction. The final evaluated result is 32.

The problem is asking to use the Distributive Property to simplify the mathematical expression and then evaluate it. The Distributive Property, in basic terms, indicates that multiplication distributes over addition or subtraction. So, for the expression 8(5 - 1), you would apply the Distributive Property as follows:

8 * 5 - 8 * 1

40 - 8

= 32

So, the equivalent expression is 40 - 8, and the evaluated result is 32.

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Answer

30+30+15+15+18+18

Step-by-step explanation:

The expression to calculate the surface area of the prism is 2 * (3 * 5 + 3 * 6 + 5* 6)

The given parameters are:

The surface area of a rectangular prism is:

Area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute known values

Area = 2 * (3 * 5 + 3 * 6 + 5* 6)

Hence, the expression to calculate the surface area of the prism is 2 * (3 * 5 + 3 * 6 + 5* 6)

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Answer:

2.871052631578947‬

Step-by-step explanation:

this is exactly the answer.

Answer:

[tex]f(x)=4(6x)[/tex]

Step-by-step explanation:

Given:

the given expression is.

[tex]f(x)=4(3)2x[/tex]

Simplify the given expression.

[tex]f(x)=4(3)2x[/tex]

[tex]f(x)=4(3\times 2x)[/tex]

[tex]f(x)=4(6x)[/tex]

Therefore, the option [tex]f(x)=4(6x)[/tex] is an equivalent function to [tex]f(x)=4(3)2x[/tex].

Answer:

[tex]y\leq 2x+4[/tex]

[tex]y\geq -x-6[/tex]

Step-by-step explanation:

step 1

Find the equation of the solid line with positive slope

we have the points

(0,4) and (-2,0)

Find the slope

[tex]m=(0-4)/(-2-0)=2[/tex]

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=2\\b=4[/tex]

substitute

[tex]y=2x+4[/tex]

step 2

Find the equation of the inequality with positive slope

we know that

The solution of the inequality, is the shaded area below the solid line

so

The equation of the inequality is

[tex]y\leq 2x+4[/tex] ----> inequality A

step 3

Find the equation of the line with negative slope

we have the points

(-6,0) and (-4,-2)

Find the slope

[tex]m=(-2-0)/(-4+6)=-1[/tex]

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=2\\point\ (-6,0)[/tex]

substitute

[tex]0=-(-6)+b[/tex]

solve for b

[tex]0=6+b[/tex]

[tex]b=-6[/tex]

so

The linear equation is

[tex]y=-x-6[/tex]

step 4

Find the equation of the inequality with negative slope

we know that

The solution of the inequality, is the shaded area above the solid line

so

The equation of the inequality is

[tex]y\geq -x-6[/tex] ----> inequality B

therefore

The system of inequalities is

[tex]y\leq 2x+4[/tex] ----> inequality A

[tex]y\geq -x-6[/tex] ----> inequality B

Answer:

[tex]radius=5\ cm[/tex]

Step-by-step explanation:

Let r be the radius of the circle and A be the area of the circle.

Given:

[tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]

And [tex]r_{2} = ?, A_{2}=78.54\ cm^{2}[/tex]

The area of a circle is directly  proportional to the square of its  radius.

A ∝ [tex]r^{2}[/tex]

[tex]A = kr^{2}[/tex]-----------(1)

Where k is the constant of proportionality

Find constant value by substituting [tex]r_{1} = 2\ cm, A_{1}=12.566\ cm^{2}[/tex]

in equation 1.

[tex]A = kr^{2}[/tex]

[tex]A_{1}=k(r_{1})^{2}[/tex]

[tex]12.566=k\times 2^{2}[/tex]

[tex]12.566=k\times 4[/tex]

[tex]k=\frac{12.566}{4}[/tex]

[tex]k=3.141[/tex]

Find [tex]r_{2}[/tex] by substituting k and [tex]A_{2}[/tex] value in equation 1.

[tex]A = kr^{2}[/tex]

[tex]A_{2}=k(r_{2})^{2}[/tex]

[tex]12.566=3.141\times (r_{2})^{2}[/tex]

[tex](r_{2})^{2}=\frac{78.54}{3.141}[/tex]

[tex](r_{2})^{2}=25.004[/tex]

where: 25.004 ≅ 25

[tex](r_{2})^{2}=25[/tex]

[tex]r_{2}=\sqrt{25}[/tex]

[tex]r_{2}=5\ cm[/tex]

Therefore; the radius of the circle is 5 cm.

Final answer:

The radius of a circle with an area of 78.54 cm² is approximately 4 cm, after setting up a proportion with a known circle area and solving for the unknown radius.

Explanation:

The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given that a circle with a radius of 2 cm has an area of 12.566 cm², we set up a proportion to find the radius of a circle with an area of 78.54 cm²:

(12.566 cm²) / (2 cm)² = (78.54 cm²) / r².

Solving for r, we find r² = (78.54 cm²) × (2 cm)² / (12.566 cm²).

After calculation, we get r approximately equal to 4 cm, rounding to the nearest whole number.

Answe

Step-by-step explanation:

he has drive 11 miles of his drive

if you divide 22 by 2 it equals 11

Good evening ,

Answer:

Step-by-step explanation:

______________________________________________________

Note:

if f is a function then each number of the domain has an unique image.

______________________________________________________

since (regarding the table) the image of 9 is 6 then the answer A is wrong

The same apply on answers B and C .

then the right answer is D(-3,-8).

:)

Answer:

dddddddddddddddddd

Divide the total number of cans by 6.

42 / 6 = 7

He bought 7 six packs.

Final answer:

Victor bought 7 six-packs of soda.

Explanation:

To find the number of six-packs of soda Victor bought, divide the total number of cans by 6. In this case, Victor bought 42 cans in total, so dividing 42 by 6 gives us 7. This means Victor bought 7 six-packs of soda.

Answer:

1500

Step-by-step explanation:

10×10=100

100×15=1500

Answer:

[tex] \frac{5}{16}, \: 31.25\%[/tex]

Answer:

the population of the city in the year 2035 is 126,226

Step-by-step explanation:

The population of a city is modeled by

[tex]P(t)= 78300(1.023 )^t[/tex]

P ( t ) represents the number of people and t is the number of years since 2014.

in the year 2014, the year t=0

we need to find the population in the year 2035

2035-2015= 21

so find population when t=21

[tex]P(t)= 78300(1.023 )^t[/tex]

[tex]P(21)= 78300(1.023 )^{21}=126226.36[/tex]

To find the exact values of cos(0), csc(0), and tan(0) given a point on the terminal side of 0, we can use the coordinates of the point to determine the values of the trigonometric functions.

To find the exact values of cos(0), csc(0), and tan(0) given that (-3,-2) is a point on the terminal side of 0, we can use the coordinates of the point to determine the values of the trigonometric functions.

First, we can find the value of cos(0) by dividing the x-coordinate (-3) by the distance from the origin, which is sqrt((-3)^2+(-2)^2). Therefore, cos(0) = -3 / sqrt(13).

Next, we can find the value of csc(0) by dividing 1 by the y-coordinate (-2). Therefore, csc(0) = 1 / -2 = -1/2.

Finally, we can find the value of tan(0) by dividing the y-coordinate (-2) by the x-coordinate (-3). Therefore, tan(0) = -2 / -3 = 2/3.

Answer:

(a). Number of protons in a chlorine atom = 17

(b). Atomic number of sodium = 11

Step-by-step explanation:

Let the number of protons in a sodium atom = x

Then, the number of protons in a chlorine atom = x + 6

Now, it is given that the atomic number of an element is equal to the number of protons per atom.

So, atomic number of sodium (Na) = x

Atomic number of chlorine (Cl) = x + 6

It is given that the atomic number of chlorine is 5 less than twice the atomic number of sodium.

∴ atomic number of chlorine (Cl) = 2 × atomic number of sodium (Na) - 5

⇒ x + 6 = 2x - 5

⇒ x - 2x = -5 - 6

⇒ -x = -11

Cancelling the minus sign from both sides, we get

x = 11

(a). Number of protons in a chlorine atom = x + 6

                                                                     = 11 + 6      (∵ x = 11)

                                                                     = 17

(b). Atomic number of sodium = x = 11

Answer:

There are 110 children total in the sports club

Step-by-step explanation:

To get this answer, its actually easier than it seems. You might need a calculator however.

First you start with the 11 children who play both badminton and squash, then, you divide that by 0.25 (25%) to get 44.

Next you take 44 and divide it by 0.4 (40%) to get 110.

And there you go! If you want to make sure you got it right simply start with 110 and multiply it by 0.4 then multiply the number/decimal you get by 0.25. You should get 11 to confirm your answer :)

The total number of miles Jean ran in the two weeks is 4.5 m.

Given that, last week Jean ran 2 fewer than 4m miles.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Here,

Number of weeks Jean ran last week = 4-2=2 m

Number of weeks Jean ran this week = 2+0.5

= 2.5 m

Total number miles = 2+2.5

= 4.5 m

Hence, the total number of miles Jean ran in the two weeks is 4.5 m.

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Answer:

1 positive solution

2.87.

Step-by-step explanation:

x^2 + 2x + 7 = 21

x^2 + 2x - 14 = 0

The product of its roots = c/a = -14 so it will have 1 positive solution.

x = -2 +/- sqrt (2^2 - 4*-14) / 2

x = -1 +/- sqrt60/2

= -1 +/- 3.873

GreATest solution is 2.87

Answer:

It has no slope because (x2-x1) in the formula [tex]m=\frac{y2-y1}{x2-x1}[/tex] is equal to zero, and the denominator of a fraction cannot be zero

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

the points (7, 10) and (7, 20)

substitute the values

[tex]m=\frac{20-10}{7-7}[/tex]

[tex]m=\frac{10}{0}[/tex] ----> is undefined

The line has a slope undefined ---> is a vertical line (parallel to the y-axis)

Answer: x≤-2

Step-by-step explanation: Solve for x. (NUMBER LINE ATTACHED)

Hope this helps you out.

The solution of the inequality is shown in figure.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 5x + 3 ≤ - 7

Now,

Solve the inequality as;

⇒ 5x + 3 ≤ - 7

⇒ 5x + 3 - 3 ≤ - 7 - 3

⇒ 5x  ≤ - 10

⇒ 5x/5 ≤ - 10/5

⇒ x ≤ - 2

Thus, The solution of the inequality is;

⇒ x ≤ - 2

Therefore, The solution of the inequality is shown in figure.

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Answer:

Step-by-step explanation:

Find the equation of the line thru the points (2,1) and (3,5)

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

This is a 2 step process. First find the slope of the line thru the points.

slope, m = diffy/diffx

m = (5-1)/(3-2)

m = 4

---------

Now use y = mx + b with either point to find b, the y-intercept.

y = mx + b

5 = 4*3 + b

b = -7

-------

Answer:

Step-by-step explanation:

Formula for calculating the equation of a line is expressed as shown below;

y = mx+c OR y-y1 = m(x-x1) where

m is the slope or gradient

c is the intercept (the point where the line cuts the y axis)

m = ∆y/∆x

m = y2-y1/x2-x1

Given the points (-8,8) and (1,-10).

x1 = -8, y1 = 8, x2 = 1, y2 = -10

m = -10-8/1-(-8)

m = -18/9

m = -2

The equation of a line can also be written as a point slope:

y-y1 = m(x-x1)

Substituting the value of x1, y1 and m into the equation we have;

y-8 = -2(x-(-8))

y-8 = -2(x+8)

y-8 = -2x-16

y= -2x-16+8

y = -2x-8

The equation of the line is y = -2x-8

Answer:

it will cost $ 14,79,000

Step-by-step explanation:

Area of the rectangular theatre  ground=L*B= 145*85= 12,325 m²

Cost of cleaning per square metre = $ 120

Total cost of cleaning = $120* 12,325= $ 14,79,000

The measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees

Solution:

Given that exterior angle of triangle is 140 degrees

The exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

Given that adjacent angles are congruent

Let one of the non adjacent interior angles be "x"

x + x = 140

2x = 140

x = 70

So the two interior angles are 70 degrees and 70 degrees

Let us find the third interior angle

The angle sum property of a triangle states that the interior angles of a triangle always add up to 180 degrees

70 + 70 + third angle = 180

third angle = 180 - 70 - 70

third angle = 180 - 140

third angle = 40 degrees

Thus the measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees

Answer:14

Step-by-step explanation:

30 students total.

7 received an a in history.

13 received an a in math.

4 received an a in both courses.

how many students did not receive an a in either course.

20 total received an a in history or math.

of these, 4 received an a in history and math.

those 4 are being counted twice.

once in history and once in math.

you need to subtract 4 from the number who got an a in history or an a in math to get a total of 16 students who got an a in history or in math.

this leaves 30 - 16 = 14 students who did not get an a in either course.

here's the breakdown.

14 students did not get an a in either course.

3 students got an a in history only.

9 students got an a in math only.

4 students got an a in both history and math.

total is 30 students.

Final answer:

To find how many students did not receive an A in either math or history, subtract the sum of students with As in both subjects (after adjusting for 4 students who received an A in both) from the total class size. It is found that 14 students did not receive an A in either subject.

Explanation:

To determine how many students didn't receive an A in either math or history, we can use the principle of inclusion-exclusion. Firstly, we have 30 students in total. We're told that 7 received an A in history and 13 in math, including four students who received an A in both subjects.

To avoid double-counting those four students, we add the number of students who received an A in history to the number who received an A in math, and then subtract the number who received an A in both:

Number of students with A in either subject: 7 (history) + 13 (math) - 4 (both) = 16 students

Then, we calculate the students who did not receive an A in either subject by subtracting those who received an A in at least one subject from the total class size:

Number of students without an A in any course: 30 (total students) - 16 (A in at least one subject) = 14 students

Therefore, 14 students did not receive an A in either math or history.

Answer: 7 bags

Step-by-step explanation:

Total no. of oranges rotten - 12

To buy no. of bags to get   -  at least 40 good oranges

No. of oranges in a bag       - 8

40  +  12 = 52 oranges

As each bag contains 8 oranges and 52 is not divisible by 8 we end up taking the closest divisible number that is 54.

If we divide 54 by 8 we get 7.

Hence Max needs to buy 7 bags of oranges.

Note: As they have asked at least 40 good oranges

Answer:

1/4

Step-by-step explanation:

There are 7 points from 0 to 7/4. This means each point represents 1/4. Therefore A is 1/4

Answer:

1/4

Step-by-step explanation:

If you count back from the 7/4, A will be at the 1/4 point.

Hope this helps :)

Answer:

(- 3, 1 )

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation of f(x)

• if c > 0 then shift up by c units

• if c < 0 then shift down by c units

Thus for f(x) - 4

(- 3, 5 ) → (- 3, 5 - 4 ) → (- 3, 1 )