Given the following functions:
f(x) = 3x
g(x) = x + 4
h(x) = x^2 - 1
Before simplifying g(f(-1)), let's first determine f(-1).
f(x) = 3x
f(-1) = 3(-1)
f(-1) = -3
g(x) = x + 4
g(f(-1)) = (-3) + 4
= -3 + 4
g(f(-1)) = 1
Therefore, the answer is 1.
These marbles are placed in a bag and twoof them are randomly drawn.What is the probability of drawing twoyellow marbles if the first one is placed backin the bag before the second draw?Give your answer as a ratio, reduced tosimplest terms.Hint: Multiply the probability of the 1st Event by theprobability of the 2nd Event to get your answer.
step 1
Find the probability that the first marble is yellow
P=2/10 ------> P=1/5
step 2
Find the probability the the second marble is yellow
P=2/10 -----> P=1/5
therefore
P=(1/5)(1/5)
P=1/25
answer is 1/25How do I solve the role of zero?f(x) = (x - 2)^5 (x + 4)^3
ANSWER
2 and -4
EXPLANATION
We are given the function:
f(x) = (x - 2)^5 (x + 4)^3
We simply need to find the zeros of the function and to do that, we need to find the values of x such that the function will be 0.
The function has already been factorised and so, we simply need to identify the zeros.
There are two zeros for the function and they are 2 and -4.
This is because when x is either 2 or -4, the function resolves to 0.
When x = 2:
[tex](2-2)^5(2+4)^3=0(6)^3\text{ = 0}[/tex]and when x = -4:
[tex](-4-2)^5(-4+4)^3=(-6)^50\text{ = 0}[/tex]And so, the zeros of the function are 2 and -4.
suppose that the maximum weight that a certain type of rectangular beam can support varies inversely as its length and jointly as its width and the sof its height. suppose also that a beam 6 inches wide, 2 inches high, and 12 feet long can support a maximum of 14 tons. what is the maximum weight that could be supported by a beam that is 4 inches wide, 3 inches high and 14 feet long
Step 1
Write the formula connecting all variables.
Weight = w
Length = L
Width = b
Height = H
k = constant
[tex]w\text{ = }\frac{kbH^2}{L}[/tex]Step 2
Use the values below to find the constant k.
b = 6
H = 2
L = 12
W = 14
[tex]\begin{gathered} 12\text{ = }\frac{k\text{ }\times\text{ 6 }\times2^2}{12} \\ 14\text{ = }\frac{24k}{12} \\ \text{Cross multiply} \\ 24k\text{ = 14 x 12} \\ 24k\text{ = 1}68 \\ k\text{ = }\frac{168}{24} \\ k\text{ = }7 \end{gathered}[/tex]Step 3
Find the unknow
W = ?
b = 4
H = 3
L = 14
[tex]\begin{gathered} W\text{ = }\frac{kbH^2}{L} \\ W\text{ = }\frac{7\text{ }\times\text{ 4 }\times3^2}{14} \\ W\text{ = }\frac{7\text{ }\times\text{ 4 }\times\text{ 9}}{14} \\ W\text{ = }\frac{252}{14} \\ W=\text{ 18 tons} \end{gathered}[/tex]The maximum weight = 18 tons
Can I Plss get some help on this (Number 50)
EXPLANATION:
Given;
We are given a rectangle with sides as indicated.
Required;
We are required to find the area and the perimeter from the dimensions provided.
Step-by-step solution;
We shall begin by reconstructing the rectangle and show the missing sides. This is done below;
Take note that we can extract one of the triangles and use the dimensions to calculate the missing side. This is also shown below;
Observe that we now have a triangle with sides 17 units and 16 units.
We draw a perpendicular and we effectively split the triangle into two right angled triangles. We can now solve for the side x using the Pythagoras' theorem.
[tex]\begin{gathered} c^2=a^2+b^2 \\ Where: \\ c=hypotenuse \\ a,b=other\text{ }sides \end{gathered}[/tex]We substitute these into the formula above;
[tex]\begin{gathered} 17^2=x^2+8^2 \\ \\ 289=x^2+64 \end{gathered}[/tex]Subtract 64 from both sides;
[tex]225=x^2[/tex]Take the square root of both sides;
[tex]\begin{gathered} \sqrt{225}=\sqrt{x^2} \\ \\ 15=x \end{gathered}[/tex]Let us now reconstruct the quadrilateral with the new dimension calculated.
We now have the Length and Width of the rectangle and we can now calculate the area and perimeter.
[tex]\begin{gathered} AREA\text{ }OFA\text{ }RECTANGLE: \\ Area=l\times w \\ \\ Area=30\times16 \\ \\ Area=480 \end{gathered}[/tex][tex]\begin{gathered} PERIMETER: \\ Perimeter=2(l+w) \\ \\ Perimeter=2(30+16) \\ \\ Perimeter=2(46) \\ \\ Perimeter=92 \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} Area=480units^2 \\ \\ Perimeter=92units \end{gathered}[/tex]Estimate the sum of the decimals below by rounding to the nearest whole number. Enter your answer in the space provided gym
Given:
[tex]5.029,8.315,5.284[/tex]Required:
Find the estimated sum of the given decimals to the nearest whole number.
Explanation:
The estimated sum by rounding to the nearest whole number is 19.
Final Answer:
The estimated sum of the given decimals by rounding to the nearest whole number is 19.
How much pesticide is need to treat 80,000 square feet at 2 pints/1000 square feetrate
2 pints ----> 1000 square feet
x pints ----> 80000 square feet
[tex]\begin{gathered} x\times1000=2\times80000 \\ 1000x=160000 \\ \frac{1000x}{1000}=\frac{160000}{1000} \\ x=160 \end{gathered}[/tex]answer:
160 pints is need to treat 80000 square feet
There are 15 members of the show choir. In how many different ways can you arrange any 8 members in the front row?
We have the following:
The first chair can be any of the 15.
For each of those ...
The second chair can be any of the 14.
For each of those ...
And so on until choosing 8 chairs
.
.
.
The eighth chair can be any of 8.
For each of those ...
Number of ways to fill the 8 chairs = (15 x 14 x 13 x 12 x 11 x 10 x 9 x 8) = 259,459,200
But in each group of 8 people you can sit on (8 x 7 x 6 x 5x 4 x 3 x 2 x 1) = 40,320 orders.
So each group of 40,320 people is represented 24 times out of 259,459,200
Therefore, the answer is:
[tex]\frac{259459200}{40320}=6435[/tex]6435 sets of 8 members, in any order.
Supposed that the mean systolic blood pressure for women I’ve age seventy is 131mmHg ( millimeters of mercury), with a standard deviation of 9 mmHg. Supposed that the blood pressure are normally distributed. Complete the following statements ( choose correct answers 68%,75%,95%,99.7%)
To answer the question, having a z-table with you will help. We can also use the 68-95-99.7 rule.
The rule states that 68.27% of a normally distributed data set is within one standard deviation of the mean, 95.45% is within two standard deviations, and 99.73% is with three standard deviations.
Given that the mean is 131 mmHg and the standard deviation is 9 mmHg, we can calculate the boundaries which are 3 standard deviations away from the mean by adding and subtracting three times the standard deviation.
[tex]\begin{gathered} 131-(3\times9)=104 \\ \\ 131+(3\times9)=158 \end{gathered}[/tex]Therefore, approximately 99.7% of women over seventy have blood pressures between 104 mmHg and 158 mmHg.
Now let's find out how many standard deviations away 122 mmHg and 140 mmHg are from the mean.
[tex]\begin{gathered} z=\frac{122-131}{9}=-1 \\ \\ z=\frac{140-131}{9}=1 \end{gathered}[/tex]122 and 140 mmHg are within 1 standard deviation of the mean. Using the 68-95-99.7 rule, we know that approximately 68.27% of women over seventy have blood pressures between 122 mmHg and 140 mmHg.
Samuel invested $210 per acre for seed, fertilizer, fuel, depreciation, and land use. If he grosses$220 per acre this year, what percent return does he earn on his investment?
Let's begin by identifying key information given to us:
Amount invested (Initial Value) = $210 /acre
Gross income (Final Value) = $220 /acre
The percentage return is given by:
[tex]\begin{gathered} Return=\frac{FinalValue-InitialValue}{InitialValue} \\ Return=\frac{220-210}{210}=\frac{10}{210} \\ Return=0.04762\approx4.76\approx4.8 \\ Return=4.8\text{\%} \end{gathered}[/tex]Therefore, the return on investment is 4.8%
△ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘. What is CA ? Enter your answer rounded to the nearest tenth in the box.
The length of the side CA is 11.84cm when the triangle is ABC and the right angle is at ∠C and the length of BC is 7.7 cm and angle A is 41°.
Given that,
The triangle is ABC and the right angle is at ∠C.
The length of BC is 7.7 cm and angle A is 41°.
We have to find the length of CA.
Take the side CA as x.
Take the trigonometric ratio.
TanA =Opposite side/ adjacent side.
Tan 41° = 7.7/ x
0.65= 7.7/x
x= 7.7/0.65
x= 11.84 cm.
Therefore, The length of the side CA is 11.84cm when the triangle is ABC and the right angle is at ∠C and the length of BC is 7.7 cm and angle A is 41°.
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Dave wants to borrow $22,000 from first finance bank. the bank will give him a 15 year loan at an interest rate od 4.85 % how mich will he pay the bank in interest over the life of the loan? Round to the nearest hundred dollar ?
Problem 7:
We determine the time as follows:
*We can proceed using the following expression:
[tex]t=\frac{\ln (\frac{m}{p})-\ln (\frac{m}{p}-\frac{r}{n})}{n\ln (1+\frac{r}{n})}[/tex]Here, t is the time it will take to pay, m is the maximum she can afford to pay each month, p is the base loan value, r is the interest rate, n is the number of periods. Now we replace:
[tex]t=\frac{\ln(\frac{500}{20000})-\ln(\frac{500}{20000}-\frac{0.071}{12})}{12\ln(1+\frac{0.071}{12})}\Rightarrow t\approx3.8[/tex]So, she will take approximately 3.8 years to pay up the loan.
Problem 8:
We determine the time he has as follows:
We use the expression:
[tex]t=\frac{\ln (\frac{m}{p})-\ln (\frac{m}{p}-\frac{r}{n})}{n\ln (1+\frac{r}{n})}[/tex]Here, t is the time it will take to pay, m is the maximum he can afford to pay each month, p is the base loan value, r is APR, n is the number of periods. Now we replace:
[tex]t=\frac{\ln(\frac{400}{14000})-\ln(\frac{400}{14000}-\frac{0.068}{12})}{12\ln(1+\frac{0.068}{12})}\Rightarrow t\approx3.3[/tex]So, he will take approximately 3.3 years to pay the loan.
Problem 10:
We determine the amount he will have to pay as follows:
*We use the following expression:
[tex]V=P(1+n)^t[/tex]Here V is the value to obtain, P is the original amount, n is the interest rate and t is the number of periods, now we replace:
[tex]V=(22000)(1-0.0485)^{15}\Rightarrow V\approx44766.09[/tex]So, after 15 years he will have to pay approximately $44766.09.
it doesn't matter which of the two points on a line you choose to call (x1,y1) and which you choose to call (x2,y2) to calculate the slope of the line . true or false.
True
Explanation
the slope of a lines is the change in y over the change in x
[tex]\text{slope}=\frac{change\text{ in y}}{\text{change in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]where
[tex]\begin{gathered} \text{P1}=(x_1,y_1) \\ P2=(x_2,y_2) \end{gathered}[/tex]Step 1
Now, to prove , make
[tex]\begin{gathered} P1(x_2,y_2) \\ P2(x_1,y_1) \\ \end{gathered}[/tex]now, replace
[tex]\begin{gathered} \text{slope}=\frac{y_1-y_2}{x_1-x_2} \\ \text{slope}=\frac{y_1-y_2}{x_1-x_2}=\frac{-(y_2-y_1)}{-(x_2-x_1)}=\frac{(y_2-y_1)}{(x_2-x_1)} \end{gathered}[/tex]and we get the same slope, it does not matter wich one of the two points we choose to call P1 and P2.
True
I hope this helps you
70% of what is 35 ???
We calculate the 70% of the number that is 35 as follows:
[tex]x=\frac{35\cdot100}{70}\Rightarrow x=50[/tex]So, the number which 70% is 35 is 50.
Instructions: Factor the polynomial expression.7x²-13x +6Answer:
Explanation
Given the polynomial
[tex]7x^2-13x+6[/tex]We can find its factors below.
[tex]\begin{gathered} 7x^2-13x+6 \\ =7x^2-7x-6x+6 \\ =7x(x-1)-6(x-1) \\ =(7x-6)(x-1) \end{gathered}[/tex]Answer: (7x-6) and (x-1)
If a savings account of $19,400 is compounded semiannually at 5,07% annual interest, how much will the account be worth in 32 months? Round your answer to thenearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
From the question, we are provided with the following information:
[tex]\begin{gathered} \text{Principal, P=\$19,400} \\ \text{Rate, r=5.07\%} \\ r=\frac{5.07}{100}=0.0507 \\ \text{Time, t(in years)=}\frac{32}{12}=2.67years \\ N\text{umber of times interest applied per time period, n=2(semi-annually)} \end{gathered}[/tex]The required parameter we are to find is the Amount, A.
Amount of a compound interest is given by the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Thus, we have:
[tex]\begin{gathered} A=19,400(1+\frac{0.0507}{2})^{2\times2.67} \\ A=19400(1+0.02535)^{5.34} \\ A=19400(1.02535)^{5.34} \\ A=19400\times1.143 \\ A=\text{ \$22,174.76} \end{gathered}[/tex]Hence, the account will be worth $22,174.76 in 32 months
geometry, please give answer i know how to I think I did the steps wrong
We get that
[tex]\begin{gathered} m\angle1+m\angle4=180\rightarrow \\ 10x+2+5x+13=180 \\ 15x+15=180 \\ 15x=165 \\ x=\frac{165}{15}=11\rightarrow \\ m\angle1=10\cdot11+2=112 \end{gathered}[/tex]The equation m = 5b represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
Determine the constant of proportionality.
10
5
1
one fifth
The constant of proportionality for the equation m = 5b is 5.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
We have,
The equation m = 5b represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
Now,
The equation:
m = 5b can be written as m ∝ b
m ∝ b
m = 5b
Where 5 is the constant of proportionality.
Thus,
The constant of proportionality for the equation m = 5b is 5.
Option B is the correct answer.
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Answer: 5
Equation of a Proportional Relationship
m = 5b
the 5 represents the constant of proportionality
the m represents the dependent variable, or y-coordinate in an ordered pair
the b represents the independent variable, or x-coordinate in an ordered pair
Reasoning Use the Distributive Property to solve the equation below. Use pencil and paper. Explain why the Distributive Property makes it possible to solve this equation. 44 - (2c + 3) = 4(C+5) + C The solution of the equation is
ANSWER and EXPLANATION
The distributive property involves simplifying expressions to make them easier to solve.
It is possible to solve the equation with distributive property because it allows us to break down equations into simpler forms of addition or subtraction.
The equation we are given is:
44 - (2c + 3) = 4(c + 5) + c
Using the distributive property, we have:
44 - 2c - 3 = 4c + 20 + c
Collect like terms:
-2c - 4c - c = 20 - 44 + 3
-7c = -21
Divide through by -7:
c = -21 / -7
c = 3
The equation has been solved.
use basic trigonometric identities to simplify the expression: -tan (-x) cot (-x) = ?
-1
Explanation
let's remember the indentities
[tex]\begin{gathered} tan\theta=\frac{sen\text{ \lparen x\rparen}}{cos\text{ \lparen x\rparen}} \\ cot\theta=\frac{cos(x)}{sin(x)} \end{gathered}[/tex]so
Step 1
let the expression
[tex]-tan(-x)cot(-x)=?[/tex]rewrite the expression:
replace using the identity
[tex]\begin{gathered} -tan(-x)cot(-x)=? \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{cos(-x)}*\frac{cos(-x)}{\sin(-x)} \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{sin(-x)}\frac{cos\left(-x\right)}{\sin(*x)} \\ -tan(-x)cot(-x)=-1*1 \\ -tan(-x)cot(-x)=-1 \end{gathered}[/tex]therefore, the answer is
-1
I hope this helps you
A car with a 15-gallon gas tank can go 22 miles on 1 gallon of gas. If the tank is full at the beginning of a 377-mile trip, how many times does the driver have to refill the gas tank?
Consider that the car can go 22 miles on 1 gallon of gas, therefore the amount of gas required for the 377 mile trip is calculated as,
[tex]\frac{377}{22}\approx17.136[/tex]So the car needs 17.136 gallons of gas to complete the trip.
Since the capacity of the tank is 15 gallons, so the driver has to fill the tank two times.
First time for the full 15 gallons refill, and the second tme for the remaining 2.136 galllons fuel refill.
Thus, the driver has to refill the gas tank 2 times, to complete the trip.
Mr. Abraham, a married man, works a 40 hour work week, 48 wooks each yoor, His hourly rate of pay is $36.60 por hour. Aftor tax deductions for his two exemptions, his bl-wookly taxablo wagos were 12,410.77. How much is deducted from each paycheck for fodoral income tax? Noto: Porcontage mothod for calculation: For taxablo bi-wooklywages over 5066, but not over $2,698 - 366,40, plus 18% of excess over $068.$200,00$278.56$283.32$294.70None of these choices are correct.
We know that the biweekly tax is equal to $65.40 plus 15% of excess over $958. In this case the excess is:
[tex]2410.77-958=1452.77[/tex]Then for this excess the tax is:
[tex]0.15\cdot1452.77=217.92[/tex]Hence the total tax is:
[tex]217.92+65.40=283.32[/tex]Therefore the answer is the third option.
1/2 to 3rd power1/2 to the 3rd power
Let's begin by identifying key information given to us:
[tex]\begin{gathered} (\frac{1}{2})^3=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{8} \\ \Rightarrow(\frac{1}{2})^3=\frac{1}{8} \end{gathered}[/tex]what is 2÷0+3×5÷5÷2000÷1000÷399
Answer:
It's basically infinity.
Step-by-step explanation:
If you just add lots of numbers along with the equation it will sometimes be infinity
I need help with this question... the correct answer choice
Given:
P(2,-4) to point P'(-2,1)
[tex]P(2-4,-4+5)=P^{\prime}(-2,1)[/tex][tex](x,y)\rightarrow(x-4,y+5)[/tex]3rd option is the correct answer.
Find the circumference of a circle with an area of 95.03 m^2. Round the answer to the nearest tenth.
The area of a circle with radius r is given by the following formula:
[tex]A=\pi r^2[/tex]The circumference of that circle is given by:
[tex]C=2\pi r[/tex]Finding the answerWe are given the area of the circle. With this data and the first formula we can construct an equation for the radius r. Once we find the radius of the circle we can use it to find its circumference. So first of all we take the first formula and we equalize it to 95.03:
[tex]95.03=\pi r^2[/tex]We can divide both sides by π:
[tex]\begin{gathered} \frac{95.03}{\pi}=\frac{\pi r^2}{\pi} \\ r^2=\frac{95.03}{\pi} \end{gathered}[/tex]Now we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{r^2}=\sqrt{\frac{95.03}{\pi}} \\ r=\sqrt{\frac{95.03}{\pi}} \end{gathered}[/tex]And that's the radius of the circle. Then we can use this value in the formula of the circumference C:
[tex]C=2\pi *\sqrt{\frac{95.03}{\pi}}=34.6[/tex]AnswerThen the answer is 34.6 m.
1,1,2,2,2,5,5,8,9,10,11
In order to calculate the median the data should be arranged in order from least to greatest.
According to this question we have the following number:
1,1,2,2,2,5,5,8,9,10,11
So, we would proceed to arrange the number as follows:
1, 1, 2, 2, 2, 5, 5, 8, 9, 10, 11
As we have a total of number of 11, then that means that the median would be the central score of it.
Therefore, in this case the central score
The temperature is recorded in 65 cities on a given day in California the average temperature is 74ﾟF with a standard deviation 4ﾟ what is the Z score for temperature of 71ﾟ
the z-score is equal to
z=(74-71)/4
z=0.75
answer is 0.75Rihanna‘s yacht holds 70 passengers. Each hour he stops at the Marnie to let some passengers off and on. The scatterplot shows how many passengers are on board during each hour of boating. Usually given line of best fit the approximate the rate of change relative to the scatterplot. Pick a point along the line and use the coordinates X, Y to plug into the X equals MX plus be equation in sulfur M. Your rate of change! What is the passengers per hour?
5
1) Examining the scatterplot we can pick two points along the best line of fit. (7,60) and (1,30)
2) So now, we can plug these points into the slope formula:
[tex]m=\frac{30-60}{1-7}=\frac{-30}{-6}=5[/tex]3) Since this is a line of best fit, we can tell that the rate of change relative is (approximately) 5.
Which of the following transformations accurately describes the relationship between the two trapezoids?A. Dilate the blue trapezoid by a scale factor of ½ to obtain the red trapezoid.B. Dilate the red trapezoid by a scale factor of 2 to obtain the blue trapezoid.C. Dilate the red trapezoid by a scale factor of ½ to obtain the blue trapezoid.D. Dilate the blue trapezoid by a scale factor of 3 to obtain the red trapezoid.
Given: Two trapezoid as shown in the image
To Determine: The transformation that relates the two trapezoids
Solution
Let us determine the coordinates of the two trapezoid as shown below
We can relate the blue trapezoid to the red trapezoid
[tex]\begin{gathered} (3,1.5)\rightarrow(6,3) \\ (4.5,1.5)\rightarrow(9,3) \\ (3,3)\rightarrow(6,6) \\ (4.5,4.5)\rightarrow(9,9) \end{gathered}[/tex]It can be observed that the transformation rule that relates the blue trapezoid to the red trapezoid is
[tex](x,y)\rightarrow(2x,2y)[/tex]It can be observed that the blue trapezoid is enlarged by a scale factor to get the red trapezoid. So, we dilate the blue trapzoid by a scale factor of 2 to get the red trapezoid.
From the options provided, the best answer related the red trapezoid to the blue trapezoid, which is a reduction by a scale factor of 1/2
Hence, the correct option is
Dilate the red trapezoid by a scale factor of 1/2 to obtain the blue trapezoid, OPTION C
Please help me with #1Please help me on my hw
The given expression is,
[tex](2x^2)^3[/tex]According to the law of exponents,
[tex]\begin{gathered} (xy)^m=x^my^m\text{ ---(a)} \\ (x^m)^n=x^{mn}\text{ ---(b)} \end{gathered}[/tex]Applying the law of exponents to the given expression,
[tex]\begin{gathered} (2x^2)^3=2^3(x^2)^3\text{ (using law (a))} \\ =8x^{2\times3}\text{ (using law (b))} \\ =8x^6 \end{gathered}[/tex]Therefore, the correct expression is
[tex](2x^2)^3=8x^6[/tex]