Answer:
-7
Step-by-step explanation:
We are given the following functions:
[tex]g(x) = x^2 + 4 + 2x[/tex]
[tex]h(x) = -3x + 2[/tex]
(g•h) (1)
The multiplication is:
[tex](g \times h)(1) = g(1) \times h(1)[/tex]
So
[tex]g(x) = 1^2 + 4 + 2(1) = 7[/tex]
[tex]h(1) = -3(1) + 2 = -3 + 2 = -1[/tex]
Then
[tex]g(1) \times h(1) = 7(-1) = -7[/tex]
So -7 is the answer.
help with algebra 1 equation pls help
Answer:
b. [tex] \blue{k = \dfrac{l - 14j}{3}} [/tex]
Step-by-step explanation:
[tex] l = 14j + 3k [/tex]
Switch sides.
[tex] 14j + 3k = l [/tex]
Subtract 14j from both sides.
[tex] 3k = l - 14j [/tex]
Divide both sides by 3.
[tex] \blue{k = \dfrac{l - 14j}{3}} [/tex]
what is the value of a+bc when a=4, b=6 and c =2? also please include how to do it step by step :)
Answer:
16
Step-by-step explanation:
a+bc
a+(b×c)
4+(6×2)
4+12
answer=16
Find the whole using the percent proportion. 70% of what number of hay bales is
63 hay bales?
Answer:
90
Step-by-step explanation:
Let the whole number be x.
100% is to x as 70% is to 63
100/x = 70/63
10/x = 10/9
10x = 90 * 10
x = 90
Answer: 90
Step-by-step explanation:
0.7x = 63, x = 63/0.7 = 90
Which of the following is the equation of a line in slope-intercept form for a
line with slope = and yintercept at (0, -1)?
O A. y - x-
1
B. y = 4x-1
O c. y= |x-1
O D. y=x+1
Answer:
y=1/4x - 1
Step-by-step explanation:
going off of the picture, I'd say this is your answer
Four students want to have their picture taken together. They will stand side-by-side for the picture. In how many different ways can the four students be arranged to take a picture?
Show your work, please :')
Answer:
24 waysStep-by-step explanation:
This is the permutation of 4:
4P4 = 4! = 1*2*3*4 = 24 ways[tex]\huge\qquad \mathbb{\fcolorbox{red}{lavenderblush}{✰Answer}}[/tex]
✶⊶⊷⊶⊷❍❁❥❀❥❁❍⊶⊷⊶⊷✶
Four students want to have their picture taken together. They will stand side-by-side for the picture. In how many different ways can the four students be arranged to take a picture
so we have to find the permutation of 4
4×3×2×124.°. In 24 different ways can the four students be arranged to take a picture
A, B, and C are collinear points:
B is between A and C.
If AB = 3x + 4, BC = 4x - 1, and AC = 6x + 5,
find AC.
9514 1404 393
Answer:
AC = 17
Step-by-step explanation:
The segment sum theorem tells you ...
AB +BC = AC
Substituting the given expressions, we have ...
(3x +4) +(4x -1) = (6x +5)
x = 2 . . . . . . . . . . . . . . . . . . subtract 3+6x from both sides
AC = 6x +5 = 6(2) +5
AC = 17
_____
AB = 10, BC = 7
HW HELP ASAP PLZZZZZ
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: (x - 5)(x - 4) }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}[/tex]
[tex] {x}^{2} - 9x + 20[/tex]
[tex] = {x}^{2} - 4x - 5x + 20[/tex]
Taking "[tex]x[/tex]" as common from first two terms and "[tex]5[/tex]" from last two terms, we have
[tex] = x(x - 4) - 5(x - 4)[/tex]
Taking the factor [tex](x-4)[/tex] as common,
[tex] = (x - 5)(x - 4)[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
help with multi step inequalities please
Answer:
B. The solution is valid because all steps to solve the inequality for F are correct.
Step-by-step explanation:
F - 32 ≤ 0
Add 32 to both sides of the equation to have;
F -32 + 32 ≤ 0 + 32
F ≤ 0 + 32
F ≤ 32
It can be observed that to solve for F, the steps are correct. Thus the solution is valid. Therefore, the correct choice in the given question is the solution is valid because all steps to solve the inequality for F are correct.
Question 31 of 50
An electrician charges (1) an initial fee of $20 and then $30 per hour. Which linear equation represents this if (h) represents hours?
f = 20h + 30
f=30h + 20
f = 50h
Answer:
ok so if it is 30 dollars per hour so 30h plus 20 so
f=30h+20
Hope This Helps!!!
Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A0 after time t. b) It is found that 8 lb of A will reduce to 4 lb in 4.6 hr After how long will there be only 1 lb left?
a) Choose the equation that gives A in terms of A0, t, and k, where k > 0.
b) There will be 1 lb left after 14 hr (Do not round until the final answer. Then round to the nearest whole number as needed.)
Answer:
(a) [tex]A = A_0 * e^{kt}[/tex]
(b) There will be 1lb left after 14 hours
Step-by-step explanation:
Solving (a): The equation
Since the substance decomposes at a proportional rate, then it follows the following equation
[tex]A(t) = A_0 * e^{kt}[/tex]
Where
[tex]A_0 \to[/tex] Initial Amount
[tex]k \to[/tex] rate
[tex]t \to[/tex] time
[tex]A(t) \to[/tex] Amount at time t
Solving (b):
We have:
[tex]t = 4.6hr[/tex]
[tex]A_0 = 8[/tex]
[tex]A(4.6) = 4[/tex]
First, we calculate k using:
[tex]A(t) = A_0 * e^{kt}[/tex]
This gives:
[tex]A(4.6) = 8 * e^{k*4.6}[/tex]
Substitute: [tex]A(4.6) = 4[/tex]
[tex]4 = 8 * e^{k*4.6}[/tex]
Divide both sides by 4
[tex]0.5 = e^{k*4.6}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.5) = \ln(e^{k*4.6})[/tex]
This gives:
[tex]-0.6931 = k*4.6[/tex]
Solve for k
[tex]k = \frac{-0.6931}{4.6}[/tex]
[tex]k = -0.1507[/tex]
So, we have:
[tex]A(t) = A_0 * e^{kt}[/tex]
[tex]A(t) = 8e^{-0.1507t}[/tex]
To calculate the time when 1 lb will remain, we have:
[tex]A(t) = 1[/tex]
So, the equation becomes
[tex]1= 8e^{-0.1507t}[/tex]
Divide both sides by 8
[tex]0.125= e^{-0.1507t}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.125)= \ln(e^{-0.1507t})[/tex]
[tex]-2.0794= -0.1507t[/tex]
Solve for t
[tex]t = \frac{-2.0794}{-0.1507}[/tex]
[tex]t = 13.7983[/tex]
[tex]t = 14[/tex] --- approximated
Find all solutions to the equation.
cos^2 x +2cosx+1=0
[tex]x= \pi[/tex]
Step-by-step explanation:
[tex]\cos^2x+\cos x+1=0[/tex]
Let [tex]u= \cos x[/tex]
Then [tex]u^2+2u+1=(u+1)^2=0[/tex]
or
[tex]\cos x = -1[/tex]
This gives us [tex]x= \pi[/tex] or all integer multiples of [tex]\pi (n \pi)[/tex]
1/3(-15 divide 1/2) 1/4 what does it equal
Answer:
-2.5 or - 2 1/2
Step-by-step explanation:
Writing out the expression Mathematically ;
1/3(-15÷1/2)1/4
Using PEMDAS :
Solving the bracket first
(-15 ÷ 1/2) = (-15 * 2/1) = - 30
We have :
1/3(-30)1/4 = - 10 * 1/4 = - 10 / 4 = - 2.5
-2.5 = - 2 1/2
John throws a biased four-sided dice.
The probabilities of getting each number are summarised in the table below.
Number
1
2
3
4
Probability
0.2
x
0.2
0.2
Work out the probability that the dice lands on 2.
Answer:
0.4
Step-by-step explanation:
0.2+0.2+0.2=0.6
1.0-0.6=0.4
This isn't 0.2 like the others which is why it's a biased dice like it says.
PLEASE ANSWER MAKE SURE YOU ARE RIGHT PLEASE I WILL MARK AS BRAINIEST
FIND THE VOLUME OF THE SPHERE
Answer:
Step-by-step explanation:
r = 1/2 unit
[tex]Volume= \frac{4}{3}\pi r^{3}\\\\=\frac{4}{3}\pi *\frac{1}{2}*\frac{1}{2}*\frac{1}{2}\\\\=\frac{1}{3}*\pi *\frac{1}{2}\\\\=\frac{1}{6}\pi[/tex]
Use the formula v = IR for current flowing through a resistor, where V is the voltage in volts, I is current in amps, and R is resistance in ohms. Find the current through a resistor with resistance 15 ohms if the voltage across it is 3 volts.
Answer:
0.2 amps
Step-by-step explanation:
Given data
The formula V=IR is the formula for ohms law
Which state that the voltage is directly proportional to the current and the resistance in an electric circuit
Now
R= 15 ohms
V= 3volts
V= IR
3= I*15
I= 3/15
I= 0.2 amps
Hence he current flowing is 0.2 amps
Can someone please answer this ASAP?
Answer:
Letter C
Step-by-step explanation:
Given:
[tex]5a+18<-27[/tex]
Subtract 18 from both sides
[tex]5a<-45[/tex]
Divide 5 from both sides to get [tex]a[/tex] alone
[tex]a<-9[/tex]
Letter C is the correct answer choice because the dot is at -9, the arrow is facing to the left, and the dot is open indicating that it's not greater/less than ""or equal to"".
Hope this is helpful
if a + b + c = 1, ab + bc + ca = -1 and abc = -1. find the value of a³+b³+c³
Answer:
1
Step-by-step explanation:
→ If we know that 3 numbers need to multiply to make -1, it must be
1, 1 and -1
→ Then we just substitute this into a³ + b³ + c³
1³ + 1³ + (-1)³ = 2 - 1 = 1
Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed. Using weight as the explanatory variable, what is the slope of a line between these two points? Answer choices are rounded to the nearest hundredth.
a. $0.13 / Ib.
b. $4.00 / Ib
c. $6.25 / Ib.
d. $7.75 / Ib.
Answer:
a. $0.13 / Ib.
Step-by-step explanation:
Slope of a line:
Suppose we have two data-points in a line. The slope is given by the change in the output divided by the change in the output.
In this question:
Input: weight(in pounds)
Output: Weekly cost to feed.
A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed.
Inputs: 0.5, 62.5
Outputs: 2, 10
Change in the outputs: 10 - 2 = 8
Change in the inputs: 62.5 - 0.5 = 62
Slope: [tex]m = \frac{8}{62} = 0.13[/tex]
So the correct answer is given by option A.
Answer:
0.13
Step-by-step explanation:
Find the zeros of the quadratic function: y = 6x2 + x – 35.
The zeros of the quadratic function: y = 6x^2 + x – 35 are x = -2.5 or x = 7/3
How to determine the zeros?The function is given as:
y = 6x^2 + x - 35
Expand the function
y = 6x^2 + 15x - 14x - 35
Factorize the function
y = (2x + 5) * (3x - 7)
Set the function to 0
(2x + 5) * (3x - 7) = 0
Split
2x + 5 = 0 or 3x - 7 = 0
Solve for x
x = -2.5 or x = 7/3
Hence, the zeros of the quadratic function: y = 6x^2 + x – 35 are x = -2.5 or x = 7/3
Read more about quadratic functions at:
https://brainly.com/question/1214333
#SPJ1
To estimate the benefits of an SAT prep course, a random sample of 10 students enrolled in the course is selected.
For each of these students, their entrance score on the exam taken at the beginning of the course is recorded. Their
exit score on the exam they take at the end of the course is recorded as well. The table displays the scores.
Answer: 57%
Step-by-step explanation:
If P = (7,-4), Find:
(180° (P)
([?], []
Enter
Step-by-step explanation:
the answer is in the above image
Assume that you purchased a new car today and financed $55,000 of the price on a 72-month payment contract with a nominal rate of 6.00%. Further, assume that you plan on paying off the balance of the car loan after you make your 48th payment. How much will your loan balance be when you pay off the car?
Answer:
The amount that your loan balance will be when you pay off the car is $20,566.18.
Step-by-step explanation:
Step 1. Calculation of monthly payment
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value or the cost of the new car = $55,000
P = Monthly payment = ?
r = Monthly nominal rate = Nominal rate / 12 = 6% / 12 = 0.06 / 12 = 0.005
n = number of months = 72
Substitute the values into equation (1) and solve for P, we have:
$55,000 = P * ((1 - (1 / (1 + 0.005))^72) / 0.005)
$55,000 = P * 60.3395139355201
P = $55,000 / 60.3395139355201 = $911.51
Step 2. Calculation of the loan amount balance when you pay off the car
This can be calculated using the ballon payment formula as follows:
P = (PV - (Ballon / (1 + r)^n)) * (r / (1 – (1 + r)^-n)) ...................... (1)
Where:
P = Monthly payment = $911.51
PV = Present value or the cost of the new car = $55,000
Ballon = Ballon payment or the loan amount balance when you pay off the car = ?
r = Monthly nominal rate = Nominal rate / 12 = 6% / 12 = 0.06 / 12 = 0.005
n = number months to pay off the loan amount balance = 48
Substituting the values into equation (1) and solve for Ballon, we have:
911.51 = (55,000 - (Ballon / (1 + 0.005)^48)) * (0.005 / (1 - (1 + 0.005)^-48))
911.51 = (55,000 - (Ballon / 1.27048916109538)) * 0.0234850290479363
911.51 / 0.0234850290479363 = 55,000 - (Ballon / 1.27048916109538)
38,812.39 = 55,000 - (Ballon / 1.27048916109538)
Ballon / 1.27048916109538 = 55,000 - 38,812.39
Ballon / 1.27048916109538 = 16,187.61
Ballon = 16,187.61 * 1.27048916109538
Ballon = $20,566.18
Therefore, the amount that your loan balance will be when you pay off the car is $20,566.18.
Which of the following is a solution of y > |x| - 5?
Answer:
download gauthmath it will help you answer this
What's the area of the trapezoid
Answer:
i dont know just study hard bro
Step-by-step explanation:
Answer:
A =36 ft^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2)h where b1 and b2 are the lengths of the bases
A = 1/2 ( 13+5) *4
A = 1/2 ( 18)*4
A =36 ft^2
How many one-to-one functions are there from the set {A, B, C} to the set {x, y, z, t, w, k}?
Answer:
120 different one-to-one functions
Step-by-step explanation:
A one-to-one function means that each element from the domain can be mapped into only one element from the range (like for a typical function), and each element from the range can be mapped only once.
This means that, for two different inputs x₁ and x₂, we can't have:
f(x₁) = f(x₂)
Because that would mean that two different values of the domain are being mapped into the same element from the range.
Ok, now that we know this, let's count the number of possible "mappings" for each element in the domain.
For the first element, A, we have the options {x, y, z, t, w, k} (a total of 6 options).
For the second element, B, we will have an option less (because one was already taken) so here we have 5 options.
For the last element on the domain, C, there will be again an option less than in the previous case, so here we have 4 options.
The total number of combinations (each combination defines a different one-to-one function) is equal to the product between all the options for each case, then the total number of one-to-one functions is:
C = 6*5*4 = 120
There are 120 different one-to-one functions.
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.365 for this random variable. (Round your answers to three decimal places.)
a. What is the probability that a drought lasts at most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
Solution :
a). P(X = x)
= [tex]$p(1-p)^x$[/tex] for x = 0, 1, 2, ....
P(x ≤ 3) = 0.837
b). Expectation = [tex]$\frac{(1-p)}{p}$[/tex]
= 1.7397
Variance = [tex]$\frac{(1-p)}{p^2}$[/tex]
= 4.7663726
Standard deviation = 2.1832
Therefore, mean + standard deviation
= 1.7397 + 2.1832
= 3.9229
[tex]$P(x > 3.9229) = 0.1626$[/tex]
So the required P = 2 x 0.1626
= 0.325
In practice, the most frequently encountered hypothesis test about a population variance is a _____. a. two-tailed test, with equal-size rejection regions b. two-tailed test, with unequal-size rejection regions c. one-tailed test, with rejection region in upper tail d. one-tailed test, with rejection region in lower tail
Answer:
c. one-tailed test, with rejection region in the upper tail.
Step-by-step explanation:
One tailed test is statistical test in which critical area of distribution is one sided and greater or less than certain value. One tailed test can be left or right sided depending on the population distribution. Rejection region of the one tailed test will determine whether to accept or reject the null hypothesis.
Solve the system 6x -2y+z= -2 2x+ 3y - 3z =11 x+ 6y=31
Answer:
x = 1
y = 5
z = 2
Step-by-step explanation:
System of equations:
6x - 2y + z = -2
2x + 3y - 3z = 11
x + 6y = 31
Isolate one variable in any of the equations:
x + 6y = 31
x = 31 - 6y
Plug in this value for x in another equation:
6(31 - 6y) - 2y + z = -2
186 - 36y - 2y + z = -2
186 - 38y + z = -2
-38y + z = -188
z = -188 + 38y
Plug in these values in the remaining equation:
2(31 - 6y) + 3y - 3(-188 + 38y) = 11
62 - 12y + 3y + 564 - 114y = 11
626 - 12y + 3y - 114y = 11
626 - 9y - 114y = 11
626 - 123y = 11
-123y = -615
y = 5
Plug in value of y into our other answers to solve for x and z:
x = 31 - 6(5)
x = 31 - 30
x = 1
z = -188 + 38(5)
z = -188 + 190
z = 2
Check your work:
6x - 2y + z = -2
6(1) - 2(5) + 2 = -2
6 - 10 + 2 = -2
-4 + 2 = -2
-2 = -2
Correct!
*Note there are several ways to solve for these types of problems. I used substitution*
The hourly earnings (in dollars) for a sample of 25 railroad equipment manufacturers are:15.60 18.7514.60 15.8014.3513.90 17.5017.5513.8014.20 19.05 15.35 15.20 19.45 15.95 16.50 16.30 15.2515.05 19.10 15.20 16.22 17.75 18.40 15.25Find the median and the mode(s)(if they exist) of the data. What is the interquartile range
Answer:
[tex]Median = 15.80[/tex]
[tex]Mode = 15.20\ \&\ 15.25[/tex]
[tex]IQR = 2.35[/tex]
Step-by-step explanation:
Given
[tex]15.60,\ 18.75,\ 14.60,\ 15.80,\ 14.35,[/tex]
[tex]13.90,\ 17.50,\ 17.55,\ 13.80,\ 14.20,[/tex]
[tex]19.05,\ 15.35,\ 15.20,\ 19.45,\ 15.95,[/tex]
[tex]16.50,\ 16.30,\ 15.25,\ 15.05,\ 19.10,[/tex]
[tex]15.20,\ 16.22,\ 17.75,\ 18.40,\ 15.25.[/tex]
Solving (a): The median and the mode
First, we sort the data.
[tex]13.80,\ 13.90,\ 14.20,\ 14.35,\ 14.60,\ 15.05,\ 15.20,\ 15.20,\ 15.25,\ 15.25,[/tex]
[tex]15.35,\ 15.60,\ 15.80,\ 15.95,\ 16.22,\ 16.30,\ 16.50,\ 17.50,\ 17.55,\ 17.75,[/tex]
[tex]18.40,\ 18.75,\ 19.05,\ 19.10,\ 19.45.[/tex]
The median position is:
[tex]Median = \frac{n + 1}{2}th[/tex]
[tex]Median = \frac{25 + 1}{2}[/tex]
[tex]Median = \frac{26}{2}[/tex]
[tex]Median = 13th[/tex]
The 13th item is: 15.80
Hence:
[tex]Median = 15.80[/tex]
The modes are:
[tex]Mode = 15.20\ \&\ 15.25[/tex] --- they both have frequency of 2 while others occur once
Solving (b): The interquartile range
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
Since the median is at the 13th position, Q1 is:
[tex]Q_1 = \frac{1 + 13}{2}th[/tex]
[tex]Q_1 = \frac{14}{2}th[/tex]
[tex]Q_1 = 7th[/tex]
The 7th item is: 15.20
[tex]Q_1 = 15.20[/tex]
Similarly, Q3 is:
[tex]Q_3 = \frac{13+n}{2}[/tex]
[tex]Q_3 = \frac{13+25}{2}[/tex]
[tex]Q_3 = \frac{38}{2}[/tex]
[tex]Q_3 = 19th[/tex]
The 7th item is: 17.55
So:
[tex]Q_3 = 17.55[/tex]
Hence,
[tex]IQR = 17.55 - 15.20[/tex]
[tex]IQR = 2.35[/tex]
What are some easy ways to find the value of
(2017^4−2016^4)/(2017^2+2016^2) without calculator
Answer:
4033
Step-by-step explanation:
An easy way to solve this problem is to notice the numerator, 2017^4-2016^4 resembles the special product a^2 - b^2. In this case, 2017^4 is a^2 and 2016^4 is b^2. We can set up equations to solve for a and b:
a^2 = 2017^4
a = 2017^2
b^2 = 2016^4
b = 2016^2
Now, the special product a^2 - b^2 factors to (a + b)(a - b), so we can substitute that for the numerator:
[tex]\frac{(2017^2+2016^2)(2017^2 - 2016^2)}{2017^2+2016^2}[/tex]We can notice that both the numerator and denominator contain 2017^2 + 2016^2, so we can divide by [tex]\frac{2017^2+2016^2}{2017^2+2016^2}[/tex] which is just one, and will simplify the fraction to just:
2017^2 - 2016^2
This again is just the special product a^2 - b^2, but in this case a is 2017 and b is 2016. Using this we can factor it:
(2017 + 2016)(2017 - 2016)
And, without using a calculator, this is easy to simplify:
(4033)(1)
4033
