Answer:
15a^5 b^10
Step-by-step explanation:
The product is 15a⁵b¹⁰.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
When multiplying two terms with the same base, you add the exponents. Therefore:
(3a²b⁷)(5a³b³) = 3 x 5 x a⁵ x b ¹⁰
= 15a⁵b¹⁰.
To learn more about the exponents;
brainly.com/question/30066987
#SPJ7
what steps do you need to do to evaluate the following expression? Select two options. –5(–2) Drag 5 sets of –2 tiles to the window. Drag zero pairs to the window. Remove the 5 groups of –2 tiles. Remove 5 negative tiles from the window.
To solve the expression given , Drag zero pairs to the window and then Remove the 5 groups of –2 tiles , Option b and c is the right answer
What is an Integer Tile method ?It is a teaching method in which materialistic representation is done for concepts like addition and subtraction .
It is used for kids who find it difficult to understand adding a negative integer etc.
For the expression given
-5 (-2)
Drag zero pairs to the window and then Remove the 5 groups of –2 tiles.
Therefore Option B and C is the right answer.
To know more about Integer Tile Method
https://brainly.com/question/18097183
#SPJ1
Find y please help !!!
Answer:
20°
Step-by-step explanation:
take the sum of 3y + 10 and y and equal it to 90° that creates an equation making it easier for you to continue
Answer:
Y = 20°let's assume the opposite angle of Y to be X
angle Y = angle X ( vertically opposite angles)
3y + 10 + X + 90° = 180° ( forming linear pair)
3y + X + 100 = 180°
X + 3y = 80° ----(1)
Y + 3y = 80°
4y = 80°
y = 20°
A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.
A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half.
Each bag of soil covers 20 square yards. How many bags should the farmer purchase?
The farmer should purchase 2 bags of soil for his farm.
What is Area of rectangle?Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.
The shape of the farm, according to the picture is a parallelogram. the total area can be calculated as follows:
Area = b X h
where
b = base
h = height
base = 6.5 + 2.5 = 9.0 yards
height = 6 yards
Area = 6 × 9 = 54 square yards.
40 square yards requires 1 bag of soil .
54 square yards will require ?
cross multiply
Bags required = 54 / 40 = 1.35 bag
Thus, the farmer will require 2 bags of soil for his farm.
learn more about area from:
brainly.com/question/21695513
#SPJ1
The length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°. What is the approximate length of the radius of the circle?
The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
Length of the arc of a circle:
s = 7.34 units
The measure of central angle:
θ = 81 degrees = 1.413 radians
s = rθ
r is the radius of the circle
7.34 = r(1.413)
r = 5.19 ≈ 5.2 units
Thus, the radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°
Learn more about circle here:
brainly.com/question/11833983
#SPJ1
Answer:
The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°
Step-by-step explanation:
What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common? Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common. Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common. Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.
The statement about both functions that is true is:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). What is the domain and range for the function of y = f(x)?The domain of a function is the set of values of input for which the function is valid.
The range is the dependent variable of a set of values for which the function is defined.
Given that:
f(x) = 4 - x
The slope (m) of the function = -1x-intercept = (4,0)y-intercept = (0,4)Domain = [4,∞)For function g(x) = -1 ×[tex]\mathbf{\sqrt{x-4}}[/tex]
The domain = x ≥ 4 and the solution set is [4,∞)The range g(x) = ≤ 0 and the solution set is [-∞, 0)The function g(x) does not have a y-intercept.Therefore, from the given options, the statement about both functions that is true is:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).Learn more about the domain of a function here:
https://brainly.com/question/1369616
#SPJ1
Answer:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Step-by-step explanation:
I got it right on the test.
Toyota manufactures most of the vehicles it sells in the United Kingdom in Japan. The base platform for the Toyota Tundra truck line is ¥1,650,000. The spot rate of the Japanese yen against the British pound has recently moved from ¥197/£ to ¥190/£. How does this change the price of the Tundra to Toyota's British subsidiary in British pounds? Explain.
When the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
Prices = 1,650,000
Exchange rates = ¥197/£
Change in exchange rate = ¥190/£
So, here Original price of the Toyota tundra is
= 1,650,000 ÷ 197
= 8375.63
New import price is = 1,650,000 ÷ 190
= 8,684.21
Percentage change in the price of the imported trucks should be
= ( New price - Old price) / old price *100 = (8,684.21 - 8375.63) ÷ 8375.63 = 3.68%
Hence , when the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
(This is the percentage change in the Japanese yen as the price of the truck remains unchanged).
Learn more about price here:
https://brainly.com/question/1153322
#SPJ10
A snowstorm started on
Tuesday at 2:12 P.M. and
ended on Wednesday at
5:46 A.M. How long did it snow in hours and minutes?
(A) 15 hours, 24 minutes
(B) 15 hours, 34 minutes
(C) 16 hours, 14 minutes
(D) 16 hours, 44 minutes
B) 15 hours, 34 minutes
2:12 + 15 hours = 5:12 A.M
5:12 + 34 minutes = 5:46 A.M
Which absolute value function defines this graph?
The vertex of the graph is at (-2, 3).
This means the equation is of the form [tex]f(x)=a|x+2|+3[/tex].
Substituting in the coordinates of one of the other points on the graph that is not the vertex, such as (-1, -1),
[tex]-1=a|-1+2|+3\\\\-1=a+3\\\\a=-4[/tex]
So, the equation is [tex]\boxed{f(x)=-4|x+2|+3}[/tex]
Evaluate: y(x+x)+3, where x=1 and y=3 A. 3 B. 10 C. 9 D. 5
Answer:
C. 9
Step-by-step explanation:
y(x+x) +3
{x= 1 , y= 3}
Putting values..
3 (1+1) +3
= 3 (2) +3
= 6 + 3
= 9
So, the option C. 9 is the correct answer.
The following data represent the number of people aged 25 to 64 years covered by health insurance (private or government) in 2018. Approximate the mean and standard deviation for age.
Age Lower Limit Upper Limit Number (millions)
25-34 25 34 26200000
35-44 35 44 33800000
45-54 45 54 33100000
55-64 55 64 29600000
Answer:
X=∑fX ∑f , where ¯X is the mean.
Mean = 115/4 = 28.75
Standard deviation = [tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex] n = the number of items = 4
Standard deviation = √28.37/4 = √7.0925 = 2.66317
Step-by-step explanation:
Mean is the number which is obtained by adding the values of all the items of a series and dividing the total by the number of items.
Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values
So, Class intervals are given here.
We have to find the middle point of the class interval.
So,
Class interval= 25- 34
Middle point= [tex]\frac{34-25}{2}[/tex]= [tex]\frac{9}{2}= 4.5[/tex]
Let's add 4.5 to the lower interval,
=> 25 + 4.5= 29.5
This is the median point and do the same for the other intervals too
i.e 39.5,49.5 and then 59.5 then multiply the number with the middle point.
So midpoint times the number. So, we get
29.5 * 21.7 = 640.15 & so on we get 129,...
Then add these numbers together. So that becomes 5375.75. And what about the total number here, that is
=>21.7 + 32.8 + 36.8 + 21.7= 118.5
So here,
Mean value, that should be equal to the sum of mean times the number divided by the total number here,
Mean= [tex]\frac{5375.75}{118.5}[/tex] = 45.36
So, this is the mean value.
Standard deviation:
Standard deviation = [tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]
[tex]\sigma[/tex] = population standard deviation
N = the size of the population
[tex]x_{i}[/tex] = each value from the population
[tex]\mu[/tex] = the population mean
So here is what we have to do,
We have to subtract the mean value from the middle point that is,
=>45.36- 21.5 and squared plus 45.36 -39.5 Squared. And plus this is 45.36 -49.5 Squared plus 45.36 -59.5 squared. And then, this is 45.
Let me just inside the apprentices Inside the practices, this is 45 .36 29.5 and take the square of this one And then add another one Which is 45.36 39.5 and then take the square this one too. And plus inside parentheses, this is 45.36 minus Which is 490.5 And then squared. That is 45.36 And -59 0.5 so And then take the square, there's 12 if you just add all of them, so we will get five 47.1184.
So the standard deviation is the square of 547, divided by The total frequency here.
Standard deviation = √28.37/4 = √7.0925 = 2.66317
Read to know more about mean and standard deviation:
https://brainly.com/question/10729938?referrer=searchResults
#SPJ10
Im stuck on this to could you guys explain how you do this
The required equation of a line is y = -3x- 1
Equation of a lineThe equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the y-intercept
Using the coordinate point (0, -1) and (-1, 2)
Slope = 2-(-1)/-1-0
Slope = 3/-1
Slope =-3
Since the line crosses the y-axis at (0, -1), hence the value of b is -1
Determine the equation
y = mx + b
y = -3x + (-1)
y = -3x- 1
Hence the required equation of a line is y = -3x- 1
Learn more on equation of a line here; https://brainly.com/question/18831322
#SPJ1
Does this relation represent a function?
Answer:
No
Step-by-step explanation:
There are multiple coordinates with the same x coordinate
Big Oil, Inc. has a preferred stock outstanding that pays an $7 annual dividend. If
investors' required rate of return is 10 percent, what is the market value of the shares?
If the required return declines to 6 percent, what is the change in the price of the stock?
The change in the price of the stock is $46.67.
How to calculate the change in price?From the information given, the current price will be:
= Annual dividend / Required rate
= 7/0.1
= $70
The market value of the shares will be:
= 7/6%
= 7/0.06
= $116.67
Therefore, the change in the price of the stock will be:
= $116.67 - $70
= $46.67
Learn more about stock on:
brainly.com/question/18124452
#SPJ1
The graph below have the same shape. What is the equation of the red graph
Answer:
G(x)=x³-1
because it intersect at the negative side of y
Answer:
g(x) = x³ - 1
(option C)
Step-by-step explanation:
We know that the shape of the graph has not changed, as stated in the question, meaning that the change has not happened as a direct change to x (like 2x³ instead of x³).
The entire graph has been moved down and not left/right, which would have happened inside the parenthesis (like g(x) = (x³ - 3)).
Because it has been shifted down (as evident by the y-intercept), and we know that the shape has not changed, we know that the original function was shifted down 1 --which can be expressed by the equation g(x) = x³-1
an airplane that is flying at an altitude of 30 000 ft is beginning to descend at a rate of 1000 feet per minute. a helicopter is beginning its trip, starting at an altitude of zero feet. the helicopter ascends more slowly than the airplane, going up at a rate of 500 feet per minute. after how many minutes will the airplane and the helicopter be at the same altitude
Based on the altitudes of both the airplane and the helicopter, the number of minutes until they are at the same altitude is 20 minutes.
When will the airplane and helicopter be at the same altitude?Assuming the minute both will be on the same altitude is x, the altitude that the airplane would be at that point is:
= 30,000 - 1,000x
The helicopter's altitude would be:
= 0 + 500x
Putting them together gives:
30,000 - 1,000x = 500x
30,000 = 1,500x
x = 30,000 / 1,500
= 20 minutes
Find out more problems on solving for altitude at https://brainly.com/question/15017805.
#SPJ1
Problem 5. Utility Bills The monthly utility bills in a city are normally distributed and
represented by the variable X, with a mean of $100 and a standard deviation of $12. Find the
probability that a randomly selected utility bill is
(a) less than $70,
(b) between $90 and $120,
(c) more than $140.
(2 points)
(2 points)
(2 points)
Hint: Convert the normal distribution X to Standard normal using Z formula Z =
and then look the Z-values from the table and then find the probability.
X-μ
6
The probabilities in the question are
0.00620.74990.000429How to solve for the probabilitiesa. For x < 70
we have
z< 70 - 100/12
= z < -30/12
= -2.5
Such that p (x<70) = 0.0062
Hence the probability that is is less than $70 = 0.0062
b. between $90 and $120,90 - 100/12. 120 - 100/12
= -0.8333 <z< 1.67
p(90<x<120) = 0.95224 - 0.20234
= 0.7499
0.7499 is the probability of between $90 and $120.
c. more than $140140-100/12
= P(Z>3.3333)
= 0.000429
Read more on probability here:
https://brainly.com/question/24756209
#SPJ1
Which of the numbers below are whole numbers?
A. 0
B. 0.388
C. 2454
D. 602.49
E. 996
F. 719557
Answer:
a whole number is a number with no decmils other than .0000 and is not a fraction where the top and bottom are equal
whole: a,c,e&f
not:b&d
Kira plans to buy a used van that costs $14,000. The dealer requires a 20% down payment. The rest of the cost is
financed with a 4-year, fixed-rate amortized auto loan at 3.5% annual interest with monthly payments.
22
Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent
if necessary. If necessary, refer to the list of financial formulas.
(a) Find the required down payment.
S
▷
$ 0
(b) Find the amount of the auto loan.
Aa
(c) Find the monthly payment.
A: 2800
B: 11200
C: 250.39 per month
The frequency table below represents the 30 best batting averages for a
semi-pro baseball league. Which ranges of batting averages were least
common among the players?
Batting Average Frequency
1
2
12
14
1
0.320-0.329
0.330 0.339
0.340 0.349
0.350-0.359
0.360-0.369
A. 0.340 0.349 and 0.350 - 0.359
B. 0.330
0.339 and 0.360 - 0.369
C. 0.320
0.329 and 0.330 -0.339
D. 0.320 0.329 and 0.360 -0.369
The ranges of batting averages were least common among the players is 0.320-0.329 and 0.360-0.369 , Option D is the correct answer.
What is meaning of Average ?Average is the middle value of a set of data points , calculated by summing all the data points and then dividing by the number of points.
It is given that , 30 best batting averages for a semi-pro baseball league.
The ranges of batting averages were least common among the players
To find this , it has to be observed that which range has the lowest frequency
The range 0.320-0.329 and 0.360-0.369 has frequency of 1 which is the least among all
Hence Option D is the correct answer.
To know more about Average
https://brainly.com/question/27646993
#SPJ1
Calculus. Please answer question attached.
(a) Given [tex]f(x) = x^3[/tex], the derivative is
[tex]f'(x)=3x^2[/tex]
which is exists for all [tex]x[/tex] in the domain of [tex]f[/tex], so [tex]]f[/tex] is differentiable everywhere and satisfies the mean value theorem. There is some number [tex]c[/tex] in the open interval (0, 2) such that
[tex]f'(c) = \dfrac{f(2) - f(0)}{2-0} \iff 3c^2 = \dfrac{8-0}2 = 4[/tex]
Solve for [tex]c[/tex] :
[tex]3c^2 = 4 \implies c^2 = \dfrac43 \implies \boxed{c = \dfrac2{\sqrt3}}[/tex]
We omit the negative square root since it doesn't belong to (0, 2). Graphically, the MVT tells us the tangent line to the curve [tex]f(x)=x^3[/tex] at [tex]x=\frac2{\sqrt3}[/tex] is parallel to the secant line through the endpoints of the given interval.
(b) [tex]f(x)=1+x+x^2[/tex] has derivative
[tex]f'(x)=1+2x[/tex]
By the MVT,
[tex]f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff 1+2c = \dfrac{7-1}2 \implies \boxed{c = 1}[/tex]
(c) [tex]f(x) = \cos(2\pi x)[/tex] has derivative
[tex]f'(x) = -2\pi \sin(2\pi x)[/tex]
By the MVT,
[tex]f'(c) = \dfrac{f(2)-f(0)}{2-0} \iff -2\pi \sin(2\pi c) = \dfrac{0-0}2 \implies \sin(2\pi c) = 0 \\\\ \implies 2\pi c = n\pi \implies c = \dfrac n2[/tex]
where [tex]n[/tex] is any integer. There are 3 solutions in the interval (0, 2),
[tex]\boxed{c = \dfrac12, c = 1, c = \dfrac32}[/tex]
(Pictured is the situation with [tex]c=\frac12[/tex])
Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][-3, 1)[/tex]Range: [tex][-5, 4][/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A cake recipe requires 4 and one-half cups of flour to make 1 cake. How many cakes can be made by a baker who has 16 cups of flour?
Answer:
3 cakes
Step-by-step explanation:
just flow by the formula then ignore the remainder and take the whole number which is 3 then that becomes your answer good day.
find the perimeter: (use 3.14 for pi):
Answer:
10.676 mm
Step-by-step explanation:
The perimeter of a circle (circumference) formula is 2*(3.14)*r. Therefore since r is 1.7, 2*3.14*1.7 = 10.676 mm.
Hope this helps!!! Please mark me as brainliest!!!
Please answer this and I will give u a cookie ;)
Answer:
m∠BAC = 40°
Step-by-step explanation:
Note that line BD passes through A, so ∠BAC and ∠CAD form a linear pair. By the Linear Pair Postulate, ∠BAC and ∠CAD are supplementary angles, and by definition their measures add to 180°:
m∠BAC + m∠CAD = 180°
Since the diagram gives us that m∠CAD = 140°, we can substitute and solve:
Starting supplementary angles definition equation ...
m∠BAC + m∠CAD = 180°
Substituting the known value of m∠CAD ...
m∠BAC + (140°) = 180°
Subtracting 140° from both sides of the equation...
(m∠BAC + 140°) - 140° = (180°) - 140°
Simplifying/evaluating...
m∠BAC = 40°
8 cm
6 cm
2 cm
Find the surface area of the rectangular prism.
Surface Area = [?]cm²
Answer:
152cm²
Step-by-step explanation:
math and stuff and things
6. Five years ago, Ross was N times as old as
Amanda was. If Amanda is now 19 years old,
how old is Ross now in terms of N?
Answer:
14N+5
Step-by-step explanation:
Five years ago; Rose Nx
Amanda x
Now; Rose Nx+5
Amanda x+5=19
x=19-5=14years
Rose(NOW) =14N+5
Alex's recipe calls for 1/3 cup of chocolate chips for every 2 cups of flour. If he increases the
amount of flour to 3 cups, how many cups of chocolate chips will he need?
Answer:
1 cup
Step-by-step explanation:
1/3 cup of chocolate chips : 2 cup of flours
So 1/3:2 = x:3
Because we want to find x, the number of how many cups of chocolate chips he needs.
you can cross multiply where you get 1/3·3=2x
which is 1=2x and x=1
Suppose the measures of the interior angles of a convex quadrilateral are four consecutive odd numbers. Find the measure of the third angle.
Answer:
91 degrees
Step-by-step explanation:
Sum of angles in a quadrilateral: 360 degrees
87, 89, 91, 93 are four consecutive odd numbers that add up to 360
third angle is 91 degrees
Emma bought 1305 bags of carrot for 16910 dollars. Find the unit rate in terms of bags per dollar.
Answer: $12.96
Given:
1305 bags of carrots purchased
Total cost = $16,910
Step-by-step explanation:
To find the unit cost, divide 16910 by 1305 to find the cost of one bag of carrots:
[tex]\frac{16910}{1305} = 12.96[/tex] (rounded to nearest hundredth)
A giant tortoise can travel 0.11 miles in 1 hour. At this rate, how long would it take the tortoise to travel 3 miles?
Answer:
about 27.27 hours.
Step-by-step explanation:
If it can travel 0.11 miles in 1 hour, we need to divide 3 miles by 0.11 miles to get the number of hours it would take to travel 3 miles. 3/0.11 is 27.27 repeating.
Hope this helps!
Answer:
27.27 hours
Step-by-step explanation:
You need to set up a proportion. I did distance over time.
[tex]\frac{.11 mi }{1 hr} = \frac{3 mi}{x hr}[/tex]
Cross multiply
.11x = 3
Divide by .11
x = 27.27
