The value of f(4) and 3[f(t)] if f(t) = 2t³ is 512 and 6t³ respectively.
What is polynomia?To calculate the polynomial expression below, we use the technique below.
From the question,
Given:
f(t) = 2t³.............. Equation 1To find f(4) we substitute 4 as the value of x in equation 1
f(4) = 2(4³)f(4) = 512.To find 3[f(t)] we multiply equation 1 by 3
3[f(4)] = 3(2t³) = 6t³Hence, the value of f(4) and 3[f(t)] if f(t) = 2t³ is 512 and 6t³ respectively.
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Kaminsky’s bronze sculpture is 5 feet in diameter, which is approximately 1.524 meters. If the sculpture was made of solid bronze, its weight could be approximated using the density of bronze , the volume, , in cubic meters, the mass, , in kilograms and applying the formula . Approximately, how many pounds would the sculpture weigh if it was made of solid bronze?
The weight of the spherical sculpture in pounds is approximately 251607 pounds
How to find the weight of the sculpture in pounds?
The sculpture is spherical and its made of solid bronze.
Therefore,
density = mass / volume
where
density = 7700 kg / m³
volume = 4 / 3πr³
volume = 4/ 3 × 3.14 × 1.524³
volume = 44.4574491494 / 3
volume = 14.8191497165 m³
Therefore,
mass = 7700 × 14.8191497165
mass = 114107.452817 kg
1 kg = 2.205 pounds
114107.452817 = ?
cross multiply
mass in pounds = 114107.452817 × 2.205
mass in pounds = 251606.933461
mass in pounds = 251607 pounds
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The product of a number and 2 is 1. Find eight times the number.
Answer:
I would think that it would be 8
Step-by-step explanation:
1-2= (-1)= -1+2=1
I think it's 8. 8 times the number of 1 is well...8.
Step-by-step explanation:
x = the number
x * 2 = 1
soooo x = 1/2
then 8 * 1/2 = 4
What is the solution set for the following equation?
x² = 16
Answer:
[tex]\{4,-4\}[/tex]
Step-by-step explanation:
[tex]~~~~x^2 = 16\\\\\implies x = \pm\sqrt{16}\\\\\implies x =\pm 4\\\\\implies x = 4 ,~ x = -4[/tex]
Answer:
x = 4
Step-by-step explanation:
x² = 16
We do the opposite of x² , so we [tex]\sqrt{x}[/tex] (square root) both sides
[tex]\sqrt{x}[/tex] = [tex]\sqrt{16}[/tex] = 4
to confirm this, we can square 4, which gets us 16.
Hope this makes sense! Feel free to ask anything further if need be.
- profparis
What are the last two digits of 1 * 2 * 3 * 4 *...*2319*2320*2321*2322 ?
Answer:
1:19
2:20
3:21
4:22
Step-by-step explanation:
I think that's the answer
Julieta models a can of ground coffee as a right cylinder. She measures its height as 6 1/4 in and its radius as 1 in. Find the volume of the can in cubic inches. Round your answer to the nearest tenth if necessary.
The volume of the cylindrical can of ground coffee is 19.6 inches cube.
How to find the volume of a cylinder?volume of the can ground coffee = πr²h
where
r = radiush = height of the cylinderTherefore,
r = 1 inches
h = 6 1 / 4 = 25 / 4 inches
volume of the can ground coffee = 3.14 × 1² × 25 / 4
volume of the can ground coffee = 78.5 / 4
volume of the can ground coffee = 19.6 inches³
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sally works in a factory that produces 1,000 televisions each day. when 40 televisions were sampled, it was found that 6 were defective. estimate how many defective televisions are made each day
An estimate of the number of defective televisions that are made each day is 150.
How many defective televisions are made each day?The first step is to determine the ratio of the televisions sampled to the total number of televisions produced each day.
1000 / 40 = 25
The second step is to multiply, 25 by 6: 25 x 6 = 150
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A regular pentagon and a square share a mutual vertex B. The sides AB and BC are sides of a third regular polygon with vertex B. How many sides does this polygon have?
There are different kinds of polygon. The number of sides that this polygon have is 5.
What is the polygon about?Note that the side of each polygon = 3.5
The parameter of polygon =17.5
Therefore the number of sides = parameter of polygon / parameter of polygon
So = [tex]\frac{17.5}{3.5}[/tex]
=5
Therefore, The number of sides that this polygon have is 5.
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Need urgent help!! It would be really appreciated if someone could help!!
Answer:
[tex]C)~ 10.06~ m[/tex]
Step-by-step explanation:
[tex]~~~~~~\sin 8^{\circ} = \dfrac{1.4}{y}\\\\\implies y = \dfrac{1.4}{\sin 8^\circ}\\\\\implies y \approx 10.06~ m[/tex]
0=x^2- 10x+10
Rewrite the equation by completing the square
[tex]~~~~~~x^2 -10x +10 =0\\\\\implies x^2 -2 \cdot 5 \cdot x +5^2 -5^2 +10 = 0\\\\\implies (x-5)^2 -25+10 = 0\\\\\implies (x-5)^2 -15=0\\\\\implies (x-5)^2 = 15[/tex]
A botanist wants to determine if a fertilizer is effective
in the growth of plants. He selects the first 100 plants
of the same type of seedling from a greenhouse and
assigns the first 50 to the group that uses the fertilizer
and remaining seedlings to the group that does not
use fertilizer. He makes sure the plants all have the
same amount of water, soil, and light for two months.
At the end of two months, he measures the heights of
the plants and finds that the ones receiving the
fertilizer are significantly taller.
Which of the following is a valid conclusion?
Inferences can be made for all plants, and the
conclusion can be drawn that the fertilizer will help
all plants grow taller.
Inferences cannot be made for all plants, and the
conclusion can be drawn that the fertilizer will help
all plants grow taller.
Inferences can be made for these types of plants,
and the conclusion can be drawn that the fertilizer
will help these types of plants grow taller.
Inferences cannot be made for these types of
plants, and the conclusion cannot be drawn that the
fertilizer will help these types of plants grow taller.
Based on the information provided, the statement which is a valid conclusion is only: option A.
What is a valid conclusion?A valid conclusion can be defined as a statement that is essentially based on empirical data, formulated hypotheses, facts, and prudent experimental design, which entails that relationship between data variables are reasonable, credible and valid.
Based on the information provided, the statement which is a valid conclusion is that the botanist can make inferences for all plants, and he can draw his conclusion that the fertilizer would help all plants grow taller.
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Answer: C
Step-by-step explanation:
Inferences can be made for these types of plants, and the conclusion can be drawn that the fertilizer will help these types of plants grow taller
Business Success Restaurant owners are continually monitoring financial aspects and customer relations of their business. They use collected data to recognize trends, predict outcomes, and plan for the future. In this task, you will play the role of a restaurant owner. You will collect data and analyze different aspects of your business. As you complete the task, keep these questions in mind: Can you predict sales based on factors such as the weather and the number of customers? Can you estimate the amount you will earn in tips on a given day based on the number of customers? Directions: Complete each of the following tasks, reading the directions carefully as you go. You may use a piece of graph paper for this task. Round all decimals to the nearest hundredths place or to the nearest cent for this task. You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all of your work and to answer each question as you complete the task. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations. Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy. Now let’s get started! Step 1: Constructing and analyzing scatterplots You keep track of the daily hot chocolate sales and the outside temperature each day. The data you gathered is shown in the data table below. Hot Chocolate Sales and Outside Temperatures Sales ($) $100 $213 $830 $679 $209 $189 $1,110 $456 $422 $235 $199 Temperature (°F) 92° 88° 54° 62° 85° 16° 52° 65° 68° 89° 91° a) Make a scatterplot of the data above. (2 points) b) Do you notice clusters or outliers in the data? Explain your reasoning. (2 points) c)How would you describe the correlation in the data? Explain your reasoning. (2 points) d) What are the independent and dependent variables? (2 points)
Answer:
They use collected data to recognize trends, predict outcomes, and plan for the future.
Step-by-step explanation:
you put $2012 into an account earning 4.345% interest compounded daily. find the amount in the account at the end of 8 years
Select the correct answer from each drop-down menu. policy is the actions taken by the to influence the real gdp and the inflation rate in the economy.
Monetary policy is the actions taken by the reserve banks to influence the real GDP and the inflation rate in the economy.
What is Monetary policy?These are actions done by the central bank of a country and involves adjusting money supply so as to achieve economic growth.
This influences the real gross domestic product and inflation rate of the country .
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Answer: Monetary and Reserve Bank
Step-by-step explanation:
;)
Does the graph show a linear function?
Answer:
The graph does show a linear function
Step-by-step explanation:
The line is decreasing at a constant rate that keeps the line straight.
Which choice represents the fraction below as a single exponential
expression?
88
O A.
(3)
OB. 811
O C. 3
OD. 85
Answer:
8^5
Step-by-step explanation:
division is just minusing exponents
The correct value of this expression is 8⁵
A fraction is also a division. When we divide power with equal bases - we subtract the exponents and keep the base.
Resolution = 8⁸/8³= 8⁸÷³= 8⁵Therefore, the answer correct is 8⁵
The scatter plot shows the relationship between the saturation specific humidity, in grams per kilogram of air, and the ambient temperature, in degrees celsius, of the atmosphere. which type of relationship would best model this data?
By critically observing the scatter plot (see attachment), the type of relationship that would best model this data is positive nonlinear.
The types of relationship in a scatter plot.In Statistics, there are four (4) main types of relationship (association) in a scatter plot and these include the following:
Positive linear association.Negative linear association.No association (None).Non-linear association.By critically observing the scatter plot shown in the image attached below, we can logically deduce that the type of relationship that would best model this data is positive nonlinear because the change in one of the variables doesn't result in a constant change in other variables.
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M(-5, 2) and N(5, 2) are the endpoints of the segment MN on the coordinate plane. What is the length of ?
A.
5 units
B.
9 units
C.
10 units
D.
12 units
This is for edmentum btw
Ten cars were recently assembled at a factory. Of these
cars, 3 will be picked at random for inspection. Of the
10 cars, 5 are blue and 5 are grey. What is the
probability that all 3 cars picked for inspection will be
blue?
Answer:
1/12
Step-by-step explanation:
Is 4,-1 a solution to y+1=3(x-4)
Answer
I don’t quite understand what your asking but I hope this helps
y=3x-13
Step-by-step explanation:
Which graph represents the function f(x))=2•(1/3)^x
Answer:
The one in the right top hand corner. It shows one arrow pointing up and one to the right.
Step-by-step explanation:
I can't really explain it.
Given that x= 7.4m and θ= 32°, work out BC rounded to 3 SF.
(not drawn accurately.)
Answer:
BC ≈ 11.8 m
Step-by-step explanation:
using the tangent ratio in the right triangle
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] , that is
tan32° = [tex]\frac{x}{BC}[/tex] = [tex]\frac{7.4}{BC}[/tex] ( multiply both sides by BC )
BC × tan32° = 7.4 ( divide both sides by tan32° )
BC = [tex]\frac{7.4}{tan32}[/tex] ≈ 11.8 m ( to 3 sf )
PLEASE HELP ASAP
solve for x
Answer:
29.44
Step-by-step explanation:
Since we know the both the measure of the angle and the adjacent line of the angle, we can use tan to find x.
tan is (Opposite/Adjacent Line)
[tex] \tan(31) = \frac{x}{49} \\ 49 \tan(31) = x \\ 29.44 = x[/tex]
That is the answer
- Kan Academy Advance
Select the correct answer. what is the solution set of y = x2 2x 7 and y = x 7? a. {(0, 7), (-1, 6)} b. {(0, 7), (-7, 0)} c. {(0, 7), (1, 8)} d. {(-2, 0), (4, 0)}
Answer:
a. {(0, 7), (-1, 6)}
Step-by-step explanation:
[tex]y = x^{2} +2x+7\\y=x+7[/tex]
subtract the equations
[tex]y = x^{2} +2x+7 \\- \ \ \ \ \ y=x+7\\y - y =x^{2} +2x+7-(x+7)\\0=x^{2} +x\\x = 0 \ and \ x= -1[/tex]
for [tex]y = x^{2} +2x+7[/tex], substitute x = 0
[tex]y = (0)^{2} +2(0)+7\\y = 0 +0+7\\y=7[/tex]
for [tex]y = x^{2} +2x+7[/tex], substitute x = 0
[tex]y = (-1)^{2} +2(-1)+7\\y = 1 -2+7\\y=6[/tex]
Answer:
A
Step-by-step explanation:
Gerrie collects honey from a few
beehives. She scoops out the honey
with a small jar that holds of a cup.
Over the last two weeks Gerrie has
filled this jar 158 times. How many
cups of honey has she collected?
The number of the cups of honey has she collected will be 52 and 2/3 cups.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Gerrie collects honey from a few beehives.
She scoops out the honey with a small jar that holds 1/3 of a cup.
Over the last two weeks, Gerrie has filled this jar 158 times.
1 small jar = 1/3 cup
But we have done this for 158 times. Then we have
158 small jar = 158 x 1/3 cups
158 small jar = 52 and 2/3 cups
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1.5 Determine the degree of the following algebraic expressions:
a. √3xyz - 5
b. y² - 3y5-y + 2y³ - 4
c. -10³
By identifying the largest exponent in each expression, we see that the answers are:
a) D = 3.
b) D = 5.
c) D = 0.
How to determine the degree of an expression?The degree is just the largest exponent of the variable in an expression.
First, we have:
a) √3xyz - 5
The largest exponent is on the term √3*xyz is 3 (because we add the 3 exponents 1 of x, y, and z) so this expression has a degree of 3.
b) y² - 3y⁵ -y + 2y³ - 4
Here the largest exponent is on the second term, so we can see that the degree is 5.
c) -10³
Here we don't have a variable, so this is a constant, which means that the degree is zero, because we could write:
-10³*x⁰
Where we use the fact that x⁰ = 1
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Which parent function is f(x)=|x|?
A The linear parent function
B The quadratic parent function
C An exponential parent function
D The absolute parent function
x^2 - 3x - 28 factor compleatly
Answer:
Step-by-step explanation:
x² - 3x - 28
What factors multiply to -28 and add to -3?
-7 and 4.
(x - 7) (x + 4)
Answer:
(x - 7)(x + 4)
Step-by-step explanation:
To find the factors, you just need to ask yourself the question: Which two numbers multiply to -28 but add to -3?
Simple guess-and-check will lead you to the numbers -7 and 4.
-7 x 4 = -28
-7 + 4 = -3
These numbers will make up the factored equation.
x² - 3x - 28
(x - 7)(x + 4)
You can check your answer by re-expanding the factored expression. This is done by multiplying each term in the first parentheses by each term in the second parentheses.
(x - 7)(x + 4) ----> x² - 7x + 4x - 28 ----> x² - 3x - 28
What is this expression in simplified form?
2√2-7√18
Answer: Heyaa! ~
Your Answer in simplified form is... −19√2
Step-by-step explanation:
2√2-7√18 = −19√2
Pull terms out from under the radical, assuming positive real numbers.
Hopefully this helps you! ~
Segment GH is shown on the graph.
What are the coordinates of the point that divides the
segment into a 3:2 ratio?
O (-7.5, 0.5)
O (0.5, -7.5)
O (-1.2,-2.2)
O (-2.2,-1.2)
The coordinates of the point that divides the segment into a 3:2 ratio is (-2.2, -1.2)
How to determine the coordinate?The points are given as:
G = (-4,3)
H = (-1,-4)
Ratio, m : n = 3 : 2
The coordinate of the point is calculated using:
[tex](x,y) = \frac{1}{m + n} * (mx_2 + nx_1, my_2 + ny_1)[/tex]
This gives
[tex](x,y) = \frac{1}{3 + 2} * (3 * -1 + 2 * -4, 3 * -4 + 2 * 3)[/tex]
Evaluate
[tex](x,y) = \frac{1}{5} * (-11, -6)[/tex]
Evaluate the product
(x,y) = (-2.2, -1.2)
Hence, the coordinate of the point is (-2.2, -1.2)
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Can anyone help? 80 points!
Answer:
D) [tex]4x^2y^3\sqrt[3]{x^2y}[/tex]Step-by-step explanation:
Given expression:[tex](8x^4y^5)^{\frac{2}{3}[/tex]Simplify in steps, using below properties of exponents:
[tex]a^ba^c= a^{b+c}[/tex] Product of Powers Property[tex](a^b)^c=a^{bc}[/tex] Power of Power PropertySolution:[tex](8x^4y^5)^{\frac{2}{3} =[/tex][tex](2^3x^4y^5)^{\frac{2}{3} =[/tex][tex]2^{\frac{3*2}{3}} x^{\frac{4*2}{3}} y^{\frac{5*2}{3}} =[/tex][tex]2^2x^{\frac{8}{3}}y^{\frac{10}{3} =[/tex][tex]4x^{2\frac{2}{3}}y^{3{\frac{1}{3} =[/tex][tex]4x^2x^{\frac{2}{3}} y^3y^{\frac{1}{3}} =[/tex][tex]4x^2y^3(x^2y)^{\frac{1}{3}}=[/tex][tex]4x^2y^3\sqrt[3]{x^2y}[/tex]Correct choice is D
Answer:
[tex]4x^2y^3\sqrt[3]{x^2y}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(8x^4y^5\right)^{\frac{2}{3}}[/tex]
Rewrite 4 as (3 + 1) and 5 as (3 + 2):
[tex]\implies \left(8x^{(3+1)}y^{(3+2)}\right)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies \left(8x^3xy^3y^2}\right)^{\frac{2}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 8^{\left(\frac{2}{3}\right)}x^{\left(3 \times\frac{2}{3}\right)}x^{\left(\frac{2}{3}\right)}y^{\left(3 \times \frac{2}{3}\right)}y^{\left(2 \times \frac{2}{3}\right)}}[/tex]
[tex]\implies 4x^2x^{\frac{2}{3}}y^2y^{\frac{4}{3}}[/tex]
[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^{\frac{4}{3}}[/tex]
Rewrite 4/3 as 1 + 1/3:
[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^{\left(1+\frac{1}{3}\right)}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^1y^{\frac{1}{3}}[/tex]
[tex]\implies 4x^2y^2y^1x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 4x^2y^{(2+1)}x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]
[tex]\implies 4x^2y^3x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies 4x^2y^3\left(x^2\right)^{\frac{1}{3}}y^{\frac{1}{3}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot c^b=ac^b:[/tex]
[tex]\implies 4x^2y^3\left(x^2y\right)^{\frac{1}{3}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]
[tex]\implies 4x^2y^3\sqrt[3]{x^2y}[/tex]