Evaluate the expression
4^2+6⋅5^2−3^3÷3^2.

Answers

Answer 1

[tex]4^2 + 6 \times 5^2- 3^3 \div 3^2.[/tex]

Evaluate exponents:
[tex]=16 + 6 \times 25- 27 \div 9[/tex]

Evaluate multiplication and division:
[tex]= 16 + 150- 3[/tex]

Evaluate addition and subtraction:
[tex]= 163[/tex]

Related Questions

Information about the age of participants in a robotics competition is below: A box plot titled "Age of Participants" and labeled "Age" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 31 on the number line. A line in the box is at 16. The whiskers end at 11 and 33. The middle 50% of the data is between what two numbers?

Answers

Final answer:

The middle 50% of the age of participants in the robotics competition falls between 13 and 31.

Explanation:

The box plot represents the age distribution of participants in a robotics competition. The box extends from the lower quartile (Q1) to the upper quartile (Q3), which in this case are 13 and 31, respectively. The line within the box represents the median, which is 16. The whiskers represent the range of the data, ending at 11 and 33.

To find the middle 50% of the data, we need to determine the values that lie between Q1 and Q3. Therefore, the middle 50% of the age of participants in the robotics competition falls between 13 and 31.

Learn more about Age distribution of participants in a robotics competition here:

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List all the pairs of integers with a product of 30

Answers

The list of pairs of integers will be created by starting with the factor pairs for 30.

1 x 30
2 x 15
3 x 10
5 x 6

Then multiply these with negative integers which will result in a positive answer.

-1 x -30 (This means the opposite of one groups of negative 30, which is posiitve 30).
-2 x -15
-3 x -10
-5 x -6

Which expression is equivalent to [log9+1/2logx+log(x^3+4)]-log6

Answers

You probably looking to write the given expression as a single logarithm.

Remember the follwing rules:

log(ab)= log(a) + log(b)
log(a/b)=log(a) - log(b)
log(a)^b = b log(a)

Based on these rules, we can write the above expression as a single logarithm, as shown below:

[tex]log(9)+ \frac{1}{2}log(x)+log( x^{3}+4)-log(6) \\ \\ =log(9)+ log(x)^{ \frac{1}{2} } +log( x^{3}+4)-log(6) \\ \\ =log( \frac{9 \sqrt{x}( x^{3}+4) }{6} ) \\ \\ =log( \frac{3 \sqrt{x}( x^{3}+4) }{2} )[/tex]

Answer:

A.) log 3 sqrt x(x^3+4)/2

Write the sum using summation notation, assuming the suggested pattern continues. 16 + 25 + 36 + 49 + ... + n2 + ...

Answers

[tex]\bf \stackrel{4^2}{16}+\stackrel{5^2}{25}+\stackrel{6^2}{36}+\stackrel{7^2}{49}+...\qquad \qquad \qquad \sum\limits_{i=4}^{\infty}~i^2[/tex]

Answer:

Hence, the sum using summation notation, assuming the suggested pattern continues [tex]16+25+36+49+......+n^2+.....[/tex] is:

[tex]\sum_{n=4}^{\infty}n^2[/tex]

Step-by-step explanation:

We have to write the sum using summation notation, assuming the suggested pattern continues:

[tex]16+25+36+49+......+n^2+.....[/tex]

Clearly we may also write this pattern as:

[tex]4^2+5^2+6^2+.....+n^2+......[/tex]

So, in terms of the summand it is written as:

[tex]\sum_{n=4}^{\infty}n^2[/tex]

( We have started our summation from 4 since the term in the summation starts with 16 which is 4^2 and goes to infinity )

require help with this question

Answers

a) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k

bi) Π₁ can be written using r = (x, y, z).
Π₁ ⇒ 3x +2y +z = 4

bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
Π₂ ⇒ 2x +3y -z = 5

c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.

A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.

The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. what is the probability that washing dishes tonight will take me between 11 and 13 minutes?

Answers

12 min 12 min 12 min 12 min

the original value of an investment is $1,800. if the value has increased by 7% each year, write an exponential to model the situation. then, find the value of the investment after 15 years

Answers

For this case we have an equation of the form:
y = A (b) ^ t
Where,
A: initial amount
b: growth rate
t: time
Substituting values we have:
y = 1800 * (1.07) ^ t
For 15 years we have:
y = 1800 * (1.07) ^ 15
y = 4966.256773 $
Answer:
An exponential to model of the situation is:
y = 1800 * (1.07) ^ t
the value of the investment after 15 years is:
y = 4966.256773 $

The value of the investment after 15 years is approximately [tex]$4,410.67.[/tex]

To model the situation where an investment of [tex]$1,800[/tex] increases by 7% each year, we can use the exponential growth formula:

[tex]\[ A = P(1 + r)^t \][/tex]

where:

-[tex]$ A $[/tex]is the amount of money accumulated after n years, including interest.

- [tex]$ P $[/tex]is the principal amount (the initial amount of money).

- [tex]$ r $[/tex]is the annual interest rate (in decimal form).

-[tex]$ t $[/tex] is the time the money is invested for, in years.

Given:

[tex]- $ P = \$1,800 $[/tex]

[tex]- $ r = 7\% = 0.07 $[/tex](as a decimal)

-[tex]$ t = 15 $[/tex] years

We substitute these values into the formula to get:

[tex]\[ A = 1800(1 + 0.07)^{15} \][/tex]

Now, we calculate the value of[tex]$ A $:[/tex]

[tex]\[ A = 1800(1.07)^{15} \][/tex]

Using a calculator, we find:

[tex]\[ A \approx 1800 \times (1.07)^{15} \approx 1800 \times 2.45037 \][/tex]

[tex]\[ A \approx \$4,410.67 \][/tex]

Therefore, the value of the investment after 15 years is approximately [tex]$4,410.67.[/tex]

Find the relative rate of change of the function f(x)=150-0.08x^2

Answers

Relative change of a function is given by it's first derivative:
The relative rate of change will be given by:
f(x)=150-0.08x^2
the first derivative is given by:
f'(x)=-0.16x
thus the answer is:
f'(x)=-0.16x

Which logarithmic graph can be used to approximate the value of y in the equation 3y = 7?

Answers

we have that
3^y = 7
applying log both members
log(3^y)=log 7
y*log 3=log 7
y=log 7/log 3

using the logarithmic graph of y=log x

I graphically determine the values for x = 3 and x = 7

see the attached figure

for x=3
log 3=0.48

for x=7
log 7=0.85

therefore
y=log 7/log 3-----> y=0.85/0.48-----> y=1.77

the answer is
the approximate value of y is 1.77

hey can you please help me posted picture of question

Answers

I think the answer is true

Answer is TRUE.

A horizontal line test will ensure that the function is one-to-one. This means each y value is paired with exactly one x-value.

If this is true for the function, we can ensure that the inverse will have exactly one x value paired with only one y value and thus will pass the horizontal line test.

Write the quotient as a mixed number. 33 ÷ 5 = 6 R2

Answers

A mixed number is a number with an integer and proper fraction.

33 / 5 = 6 R3 which is equal to 6 and 3/5

Let f be a function of two variables that has continuous partial derivatives and consider the points a(7, 3), b(12, 3), c(7, 7), and d(15, 9). the directional derivative of f at a in the direction of the vector ab is 5 and the directional derivative at a in the direction of ac is 4. find the directional derivative of f at a in the direction of the vector ad. (round your answer to two decimal places.)

Answers

The directional derivative of a function [tex]f(x,y)[/tex] in the direction of [tex]\mathbf v[/tex] is given by

[tex]\nabla f(x,y)\cdot\mathbf v[/tex]

We have [tex]\vec{ab}=\mathbf b-\mathbf a=(12-7,3-3)=(5,0)[/tex], so that [tex]\|\vec{ab}\|=5[/tex], at which point we're given

[tex]\nabla f(7,3)\cdot\dfrac{(5,0)}5=5\implies1\cdot\dfrac{\partial f}{\partial x}(7,3)+0\cdot\dfrac{\partial f}{\partial y}(7,3)=5[/tex]

[tex]\implies\dfrac{\partial f}{\partial x}(7,3)=5[/tex]

We're also given that, in the direction of [tex]\vec{ac}=\mathbf c-\mathbf a=(7-7,7-3)=(0,4)[/tex] with [tex]\|\vec{ac}\|=4[/tex], we have

[tex]\nabla f(7,3)\cdot\dfrac{(0,4)}4=4\implies0\cdot\dfrac{\partial f}{\partial x}(7,3)+1\cdot\dfrac{\partial f}{\partial y}(7,3)=4[/tex]

[tex]\implies\dfrac{\partial f}{\partial y}(7,3)=4[/tex]

So in the direction of [tex]\vec{ad}=\mathbf d-\mathbf a=(15-7,9-3)=(8,6)[/tex], with [tex]\|\vec{ad}\|=10[/tex], we have

[tex]\nabla f(7,3)\cdot\dfrac{(8,6)}{10}=\dfrac1{10}(4,4)\cdot(8,6)=9.60[/tex]

To answer this question, it is necessary to make use of the concepts of directional derivative and gradient of a function.

The solution is:

grad F( x, y ) ×ad(u) =64/10

The gradient of a function f (x,y) is a vector defined by:

grad f(x,y) = δf(x,y)/δx × i + δf(x,y)/δy × j

and directional derivative, in the direction of ab is defined by :

grad f( x,y) × Uᵃᵇ(u) (1) where Uᵃᵇ is a unitary vector in the direction of ab

according to that Uᵃᵇ (u) = Uᵃᵇ/|ab|

Then if the directional derivative of f (x,y) in the direction of the vector ab is 5.

A ( 7 , 3 ) B ( 12 , 3 ) then vector ab is:

ab = [ 12 - 7 , 3 - 3 ] ⇒ ab = [ 5 , 0 ] and |ab| = √ (5)² (0)² |ab| = 5

a unitary vector in the direction of ab is:

ab(u) = 5×i/ 5 and according to equation (1)

δf(x,y) / δx × i × 5 × i / |5| = 5

δf(x,y) / δx × i × 5 × i = 25

δf(x,y) / δx = 5 then f( x,y ) = 5 × x + ????

We go on to calculate the component on j of f(x,y)

Following the same procedure

ac = ( 7 , 7 ) - ( 7 , 3 ) ⇒ ac = [ 0 , 4 ] |ac| = √(4)² + (0)²

|ac| = 4

Unitary vector in the direction of ac(u) is:

ac/|ac| = 4 × j / 4

Then :

δf(x,y) / δy × j × + 4 × j / 4 = 4

δf(x,y) / δy × j × + 4 × j = 16

δf(x,y) / δy = - 4 and f(x,y) = -4×y

f(x,y) = 5 × i + 4 × j

Finally:

vector ad = [ ( 15 - 7 , 9 - 3 ) ] ⇒ ad = ( 8 , 6 )

Unitary vector in direction ad is

ad(u) = ( 8 ×i + 6 ×j ) / √ (8)² + (6)² ⇒ ad(u) = ( 8 ×i + 6 ×j ) /√ (8)² + (6)²

ad(u) = ( 8 ×i + 6 ×j ) /10

Now we have f (x,y ) = 5 × i + 4 × j and ad(u) = ( 8 ×i + 6 ×j ) /10

We can calculate the directional derivative of f(x,y) in the direction of ad with the use of equation (1)

grad F( x, y ) ×ad(u) = ( 5 × i + 4 × j ) × ( 8 ×i + 6 ×j ) /10

grad F( x, y ) ×ad(u) = 4 + ( 24/10)

grad F( x, y ) ×ad(u) =64/10

Related Link :https://brainly.com/question/7638557

hey can you please help me posted picture of question

Answers

The discriminant can be determined from the number of roots of the graph.

If Disc> 0, the function has two distinct roots
If Disc = 0, the function has a repeated root
If Disc < 0, the function has no real root.

Since, the given function has two distinct roots i.e. it cross x-axes at two different points, its discriminant will be positive.

So, the answer to this question is option C

Yes he’s right it’s positive infinity so it’s C

hey can you please help me posted picture of question

Answers

For this case we have the following function transformation:
Horizontal translations:
Suppose that h> 0:
To graph y = f (x + h), move the graph of h units to the left.
Answer:
option B

Addition of a number to x as is done in F(x+6) results in a shift towards left direction of the original function. Since G(x) = F(x+6) , G(x) is obtained by moving F(x) 6 units to left.

So, G(x) is F(x) shifted 6 units to the left.

Thus, the correct answer is option B

To choose a mascot for a new middle school, 8th-grade students were polled, and their top choice was selected as the mascot. Was the sample a biased sample?

Answers

The sample is biased because only 8th-grade students were polled and the choice of 8th grade students might not be the representative choice of other grades in the middle school.

Answer:

Yes, the sample was biased.

Step-by-step explanation:

We are told that to choose a mascot for a new middle school, 8th-grade students were polled, and their top choice was selected as the mascot.

We know that an unbiased sample is an accurate representation of the entire population and it can help us draw conclusions about the population.

For an unbiased sample each member of a population should equally likely to be chosen and the sample should be representative of the population as a whole.

For an unbiased sampling for mascot students should be chosen randomly from each grade of the middle school.

Since all the students were polled from the same grade, so their choice can not represent the choices of all the students of the school, therefore, the sample was a biased sample.

hey can you please help me posted picture of question

Answers

Option B is the correct answer.

The solution is listed below:

[tex]3 x^{2} +27 \\ \\ =3( x^{2} +9) \\ \\ =3( x^{2} +3^{2}) \\ \\ =3( x^{2} -(3i)^{2}) \\ \\ =3(x-3i)(x+3i) \\ \\ =(3x-9i)(x+3i) [/tex]

six friends are going to buy a pizza. Their chices are to biu 2 medium 10-inch diameter pizzas for 7:00 each, or 1 large 14 inch diameter pizza for 15.00. Both prices include tax and tip. The friends agree that their best choice is the one that gives them the most pizza for their money. which is the best choice?

Answers

For this question, we want to find out the greatest amount of area of pizza for the least amount of money:

So we have two pizzas with a 10 in. diameter. Let us take one of those pizzas.

The formula for area of a circle is [tex] \pi r ^2[/tex]; So the area for one of these 10 in. pizzas would be [tex] \pi (5)^2[/tex] or 25[tex] \pi [/tex].

We have two of these pizzas, so the total area that we would get with $14 would be 25[tex] \pi [/tex]*2 or 50[tex] \pi [/tex].

For the second case, we have one pizza with a 14 in. diameter.

The area of this pizza will be [tex] \pi (7)^2[/tex] or 49[tex] \pi [/tex].

So for $15 we can buy 49[tex] \pi [/tex] worth of pizza.

The best deal would be to buy the two medium pizzas of 10 inch diameter, because for $14, you get 50[tex] \pi [/tex].

Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?

Answers

We have to find value of the house in 8 years so we will plug t=8 years in given equation.

[tex] y=150000(1.004)^{\left(12t\right)} [/tex]

[tex] y=150000(1.004)^{\left(12*8\right)} [/tex]

[tex] y=150000(1.004)^{96} [/tex]

[tex] y=150000(1.46702133432) [/tex]

[tex] y=220053.200148 [/tex]

Hence house will worth approx $220053.20 in 8 years.

Solution:

Equation of the appreciation of the value of house is given by:-

[tex]y=150000(1.004)^{12t}[/tex]

We need to find the worth of the house after 8 years

So, that means time, t=8

Let us plug t=8 in the equation [tex]y=150000(1.004)^{12t}[/tex]

So, we get,

[tex]y=150000(1.004)^{12*(8)}[/tex]

[tex]y=150000(1.004)^{96}[/tex]

[tex]y=150000(1.467021)[/tex]

y=150000*1.467021

y=220053.20

In 8 years the value appreciates to $220053.20, that s, worth of house after 8 years=$22005320

What is 84%, percent of 300?

Answers

300/x=100/84
(300/x)*x=(100/84)*x - we multiply both sides of the equation by x
300=1.19047619048*x - we divide both sides of the equation by (1.19047619048) to get x
300/1.19047619048=x
252=x
x=252

100% =300
84%= 252
You have to multiply 84x300, then divide it by 100.

Miles had a piece of paper 1/4 of a large circle cut in three equal parts from the center point of the circle. What angle is the measure of each part?

Answers

The angle of 1/4 of a circle is given by:
(1/4) * (360) = 90 degrees
We now look for the angle that results from dividing 1/4 of a circle into three equal parts.
We have then:
(1/3) * (90) = 30 degrees.
Answer:
the measure of each part is:
30 degrees

The measure of the each part of the large circle is 90 degrees.

What is the measue of each part?

A circle is a bounded figure which points from its center to its circumference is equidistant. The sum of angles in a circle is 360 degrees.

Measure of the angle of each part = 1/4 x 360 = 90 degrees

To learn more about a circle, please check: https://brainly.com/question/14351152

Sherrod deposits $500 each year in a savings account earning 3% interest compounded annually. He makes no withdrawals. How much interest will the account earn after 3 years?

Answers

The formula for annual compound interest, including principal sum, is:
A = P (1 + r/n) (nt)

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (500)
r = the annual interest rate (.03)
n = the number of times that interest is compounded per year (1)
t = the number of years the money is invested (3)

A=5000(1+.03/1)^1(3)

A=546.36

Interest (I) gained is A-P

I=546.36-500

I=46.36

Javier is evaluating the expression (-8)[10 + (-5) + (-8)]

Multiplying the numbers 10, -5, and -8 by a certain number and then adding the three products together will give Javier the fully simplified evaluated expression. What is that number?

Answers

Final answer:

The number that will give Javier the fully simplified evaluated expression is 24.

Explanation:

To evaluate the expression (-8)[10 + (-5) + (-8)], we need to multiply the numbers inside the parentheses by a certain number and then add the three products together. Let's solve it step by step:

Multiplying -8 by 10: (-8) * 10 = -80Multiplying -8 by -5: (-8) * (-5) = 40Multiplying -8 by -8: (-8) * (-8) = 64Add the three products: -80 + 40 + 64 = 24

Therefore, the number that will give Javier the fully simplified evaluated expression is 24.

There are approximately 2.6 million deaths per year in country A. Express this quantity as deaths per minute.

Answers

Take 2.7 million divided by the number of minutes in a year. 1 hour= 60 minutes 1 day= 24 hours So you take 24 hours × 60 minutes =1440 minutes 1 year= 365 per minute.

In one year, there are 365 days
365x24=8760 hours
8760x60=525 600 minutes

Dividing 2.6 million to the last number (525 600), we find death per minute in this country, which gives us more than 4 deaths in a minute.

hey can you please help me posted picture of question

Answers

To remove the the complex number from the denominator we multiply and divide the entire expression with the conjugate of denominator.

The conjugate of 1 - 4i is 1 + 4i

So, we can write:

[tex] \frac{2+i}{1-4i}* \frac{1+4i}{1+4i} \\ \\ = \frac{2+8i+i-4}{1+16} \\ \\ =\frac{-2+9i}{17} \\ \\ = \frac{-2}{17} + \frac{9i}{17} [/tex]

So, the correct answer is option B

A car dealer buys a new car for $24,500. The dealer then marks the car's price up 27%
What is the selling price of the car?

Answers

the new price of the car is $31,115

hope this helped. please mark as brainliest!

PLZ HELP ASAP TANGENTS OF CIRCLES

Answers

First, we are given that the inscribed angle of arc CB which is angle D is equal to 65°. This is half of the measure of the arc which is equal to the measure of the central angle, ∠O.

m∠O = 2 (65°) = 130°

Also, the measure of the angles where the tangent lines and the radii meet are equal to 90°. The sum of the measures of the angle of a quadrilateral ACOB is equal to 360°.

m∠O + m∠C + m∠B + m∠A = 360°

Substituting the known values,
130° + 90° + 90° + m∠A = 360°

The value of m∠A is equal to 50°.

Answer: 50°

simplify 5p2 5p3?
whats the answer

Answers

5p5 but the five at the end is small

Hi there!

[tex] \frac{ {5p}^{2} }{5 {p}^{3} } = \frac{5}{5p} = \frac{1}{p} [/tex]
Answer C.

Explanation:
First divide the expression by p^2 and second divide by 5. Now we've found the simplified expression and our answer.

~ Hope this helps you!

Lisa has a scholarship that pays 75% of her tuition for all four years she attends college. What is the total amount the scholarship is worth if Lisa's classes cost 12,000 per year

Answers

Since you're given the total cost per year (12,000) you multiply it by 4 so that you get the total amount for the four years. e.g. (4 x 12,000) = 480,000
Now you calculate the 75% from this amount because we want to obtain the amount of money the scholarship is worth. That is 480,000 x 75% = 360,000
or 480,000 x 0.75 = 360,000
So, the scholarship is of 360,000

For a popular Broadway musical, theater box office all $356 apiece 275, tickets and $60 apiece, and 369 tickets and $45 apiece. How much money did the box office ticket Take in?

Answers

Answer: $ 61,585

Explanation:

Since the question is incomplete and confusing, here I rephrase it:

A theater box office sold:

   356 tickets at $80 apiece,
     275 tickets at $60 apiece, and
   369 tickets at $45 apiece.

How much money did the box office take in?

The problem is solved by multiplying the number of tickets at each price and adding all the partial sums:

This is:

356 tickets × $80 / ticket = $28,480
275 tickets × $ 60 / ticket = $16,500
369 tickets × $45 / ticket = $16,605

Sum = $28,840 + $ 22,000 + $ 16,605 = $ 61,585

Answer: $ 61,585
If this is what your question means, then;

1. 356 tickets at $80 apiece2. 275 tickets at $60 apiece3. 369 tickets at $45 apiece
Just multiply the number of tickets per class to its corresponding price:356 tickets * $80 / ticket = $28,480275 tickets * $ 60 / ticket = $16,500369 tickets * $45 / ticket = $16,605
Total = $28,840 + $ 22,000 + $ 16,605
Total = $ 61,585
The total earnings is $ 61,585

hey can you please help me posted picture of question

Answers

im sure that it is A. i hope this helps you and you make a great grade on your test

Answer:
The solutions are: 1 + 6i and 1 - 6i

Explanation:
The general form of the quadratic equation is:
ax² + bx + c = 0

The given equation is:
x² - 2x + 37 = 0

By comparison:
a = 1
b = -2
c = 37

Now, to get the solutions of the equation, we will use the quadratic formula shown in the attached image.

By substitution in this formula, we would find that:
either x = [tex] \frac{2+ \sqrt{(-2)^2-4(1)(37)} }{2(1)} = 1 + 6i[/tex]

or x = [tex] \frac{2- \sqrt{(-2)^2-4(1)(37)} }{2(1)} = 1 - 6i[/tex]

Hope this helps :)

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Evaluate the expression 4^2+6⋅5^2−3^3÷3^2.

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Evaluate the expression
4^2+6⋅5^2−3^3÷3^2.