Answer:
7 groups can be made each with five people :)
What is the yintercept of the function, represented by the table of values below?
A. 9
B. 3
C. 6
D. 12
Answer:
A. 9
Step-by-step explanation:
First find the slope (m) using two given pairs of values form the table, say (1, 6) and (2, 3):
Slope (m) = change in y/change in x
Slope (m) = (3 - 6)/(2 - 1) = -3/1
Slope (m) = -3
Next, substitute (1, 6) = (x, y) and m = -3 into y = mx + b and solve for y-intercept (b).
Thus:
6 = -3(1) + b
6 = -3 + b
Add 3 to both sides
6 + 3 = -3 + b + 3
9 = b
b = 9
y-intercept = 9
4. As part of your retirement planning, you purchase an annuity that pays 4 % annual
interest compounded quarterly
a. If you make quarterly payments of $900 how much will you have saved in 5
years?
b. Instead, if you make quarterly payments of $450, how much will you have saved
in 10 years?
9514 1404 393
Answer:
a. $19817.10
b. $21998.87
Step-by-step explanation:
The formula for the future value of an annuity with payments "A" and interest at rate r compounded quarterly for t years is ...
FV = A((1 +r/4)^(4t) -1)/(r/4)
The attachment shows this evaluated for ...
a. A = 900, r = 0.04, t = 5. FV = $19817.10
b. A = 450, r - 0.04, t = 10. FV = 21,998.87
giúp mình với mình không biết làm
Which equation is equivalent to 15-7x=14
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{15 - 7x = 14}[/tex]
[tex]\large\text{-7x + 15 = 14}[/tex]
[tex]\underline{\large\text{SUBTRACT 15 to BOTH SIDES}}[/tex]
[tex]\large\text{-7x + 15 - 15 = 14 - 15}[/tex]
[tex]\underline{\underline{\large\text{CANCEL out: 15 - 15 because that gives you 0}}}[/tex]
[tex]\underline{\underline{\large\text{KEEP: 14 - 15 because that helps solve for the x-value}}}[/tex]
[tex]\large\text{14 - 15 = \bf -1}[/tex]
[tex]\underline{\underline{\underline{\large\text{NEW EQUATION: -7x = -1}}}}[/tex]
[tex]\underline{\large\text{DIVIDE -7 to BOTH SIDES}}[/tex]
[tex]\mathsf{\dfrac{-7\mathsf{x}}{-7}=\dfrac{-1}{-7}}[/tex]
[tex]\underline{\underline{\large\text{CANCEL out: } \dfrac{-7}{-7} \large\text{ because that gives you 1}}}[/tex]
[tex]\underline{\underline{\large\text{KEEP: }\dfrac{-1}{-7}\large\text{ because helps you get the x-value}}}[/tex]
[tex]\mathsf{x = \dfrac{-1}{-7}}[/tex]
[tex]\mathsf{x = \dfrac{-1\div-1}{-7\div-1}}[/tex]
[tex]\mathsf{x =\bf \dfrac{1}{7}}[/tex]
[tex]\boxed{\boxed{\large\text{Therefore, your answer is: \bf x = }\bf \dfrac{1}{7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
what is the area of a triangle of base 10m and height of 8m
Answer:
40m
Step-by-step explanation:
to find the area of a triangle you must do bh/2
So you do 10 times 8 which is 80.
Then you do 80 divided by 2 which is 40.
I hope this helps!
Let f(x) = 2x2 + x − 3 and g(x) = x + 2.
Find (f • g)(x)
Answer:
[tex](f\cdot g)(x) = 2x^3 + 5x^2-x-6[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=2x^2+x-3\text{ and } g(x)=x+2[/tex]
And we want to find:
[tex](f \cdot g)(x)[/tex]
Recall that this is equivalent to:
[tex]=f(x)\cdot g(x)[/tex]
Substitute. Hence:
[tex](f\cdot g)(x)= (2x^2+x-3)(x+2)[/tex]
Expand if desired:
[tex]\displaystyle = x(2x^2+x-3)+2(2x^2+x-3) \\ \\ = (2x^3+x^2-3x)+(4x^2+2x-6) \\ \\\ = 2x^3 + 5x^2-x-6[/tex]
Answer:
2x^3+5x^2-x-6
Step-by-step explanation:
f(x) = 2x^2 + x − 3 and g(x) = x + 2.
(f • g)(x) = (2x^2 + x − 3 ) * (x + 2)
Distribute
= (2x^2 + x − 3 )*x + (2x^2 + x − 3 )*2
= 2x^3 +x^2 -3x + 4x^2 +2x -6
Combine like terms
=2x^3+5x^2-x-6
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the Empirical Rule rule, what is the approximate percentage of cars that remain in service between 36 and 39 months
Answer:
The approximate percentage of cars that remain in service between 36 and 39 months is of 2.35%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 45 months, standard deviation of 3 months.
What is the approximate percentage of cars that remain in service between 36 and 39 months?
36 = 45 - 3(3)
39 = 45 - 2(3)
So within 2 and 3 standard deviations below the mean.
99.7 - 95 = 4.7% of the measures are between 2 and 3 standard deviations of the mean, however, this is two-tailed, considering both above and below the mean.
In this case, both 36 and 39 are below the mean, and due to the symmetry of the normal distribution, this percentage is divided by half, so 4.7/2 = 2.35.
The approximate percentage of cars that remain in service between 36 and 39 months is of 2.35%.
Course Activity: Sides and Angles of Congruent Triangles Part C Measure the lengths of the sides of ∆ABC and its three images and record the measurements in the table.
Answer
Step-by-step explanation:
Using the net below, find the surface area
of the rectangular prism.
5 cm
5 cm
2 cm
5 cm
5 cm
2 cm
2 cm
2 cm
Surface Area =
Answer:
Surface area = 90 cm²
Step-by-step explanation:
Given net of the rectangular prism shows the dimensions as,
Length = 5 cm
Width = 5 cm
Height = 2 cm
`Expression for the surface area of a rectangular prism = 2(lb + bh + hl)
Here, l = length
w = width
h = height
By substituting the values in the expression,
Surface area = 2(5×2 + 5×2 + 5×5)
= 2(10 + 10 + 25)
= 90 cm²
Answer:
Step-by-step explanation:
What is the value of the digit in the hundred thousands place?
11,391,243
A. 100,000
B. 300,000
C. 90,000
D. 10,000,000
Answer:
B, 300,00
3-1st
4-10th
2-100th
1- 1000th
9-10,000th
3-100,000th
Answer:
B. 300,000
Step-by-step explanation:
1a and b. Plz show ALL STEPS like LITERALLY ALL STEPS
Answer:
See step by step
Step-by-step explanation:
1a.
[tex] \frac{7\pi}{3} [/tex]
Coterminal Angles difference or a full revolution or 2 pi. so it standard position will be
[tex] \frac{7\pi}{3} - \frac{6\pi}{3} = \frac{\pi}{3} [/tex]
The expression will be
[tex] \frac{\pi}{3} + 2\pi \times n[/tex]
where n is the interger number of revolutions.
1b. Instead using radians, we will be using degrees.
Coterminal Angles difference will be 360 degrees. so it standard position within the unit circle will be
[tex] - 100 + 360 = 260[/tex]
The expression is
[tex] - 100 + 360 \times n[/tex]
where n is the interger number of revolutions.
44 and 45 are alternate interior
angles. Find the measure of 44.
t
115/65°
43/44
44 = [?]
t
45/46
47/48
274
Fnter
Answer:
115
Step-by-step explanation:
The opposite angles (115degree angle and angle 4) are equal.
Angle 3=65
Angle 4=115
Angle 5=115
Angle 6=65
Angle 7=65
Angle 8=115
Brainliest please~
To find the distance AB across a river, a distance BC of 415 m is laid off on one side of the river. It is found that B = 112.2° and C = 18.3°. Find AB.
The distance AB across the river is approximately 171.4 meters
The known parameters are;
The distance BC laid off on one side of the river = 415 m
The measure of ∠B = 112.2°
The measure of angle ∠C = 18.3°
The unknown parameter;
The distance AB across the river
Strategy;
Taking the points A, B, and C, being the vertices of the triangle, ΔABC, and apply sine rule to find distance AB;
By the angle sum property, the measure of angle, ∠A = 180° - (∠B + ∠C)
∴ ∠A = 180° - (112.2° + 18.3°) = 49.5°
By sine rule, we get;
[tex]\mathbf{\dfrac{a}{sin (\alpha)} = \dfrac{b}{sin (\beta)} = \dfrac{c}{sin (\gamma)}}[/tex]
Therefore;
[tex]\mathbf {a = sin (\alpha) \times \dfrac{b}{sin (\beta)}}[/tex]
Plugging in α = AB, [tex]\alpha[/tex] = ∠C = 18.3°, b = BC = 415, β = ∠A = 49.5°, we get;
[tex]AB = sin (18.3 ^{\circ}) \times \dfrac{415}{sin (49.5^{\circ})} \approx 171.4[/tex]
The distance across the river, AB ≈ 171.4 m
Learn more about sine rule here;
https://brainly.com/question/15018190
Si se duplica la base de un triángulo, ¿su área se reduce a la mitad? Justificar.
Answer:
Dado que el área de un triángulo es igual a la multiplicación de su base por su altura, si la base de un triángulo se duplica, su área se incrementará, con lo cual la afirmación es incorrecta, ya que el área no se reducirá a la mitad. Así, por ejemplo, un triángulo de base 10 y altura 15 tendrá un área de 50 (10 x 5), mientras que si su base se duplica a 20, pasará a tener un área de 100 (20 x 5), con lo cual su área también se duplicará.
ASAP!!!!!! SHOW WORK!!!! Thank you
Answer:
y = -6Step-by-step explanation:
If the three points are collinear, the slopes of RS and ST are same:
m(RS) = (4 - 8)/(1 + 1) = -4/2 = -2m(ST) = (y - 4)/(6 - 1) = (y - 4)/5Since the sloes are equal we have the following equation:
(y - 4)/5 = -2y - 4 = -10y = -10 + 4y = -6Slopes must be equal
slope of RS
m=4-8/1+1m=-4/2m=-2Now
Slope of ST=-2
y-4/6-1=-2y-4/5=-2y-4=-10y=-10+4y=-6A jar of gumballs contains 4 reds, 2 greens, and 6 blues. What is the probability of getting two blues in a row without replacement?
Select one:
a. 3/4
b. 1/2
c. 5/22
d. 5/11
Answer:
C
Step-by-step explanation:
Hypergeometric distribution
[tex]\frac{{6\choose2}}{{12\choose2}}=\frac{15}{66}= \frac{5}{22}[/tex]
A store sells 5 different shirts, 6 different pants, 3 different shoes, and 9 different socks. You are making an outfit with one of each article of clothing. How many outfits can you make?
Answer:
you can make 3 outfits
Step-by-step explanation:
because,if you just have 3 shoes aotomaticly you just wear 3 shirt and 3 pants.
for the socks, one people wear 2 socks so there you have 3 outfits
Answer:
[tex]810[/tex]
Step-by-step explanation:
For each shirt, there are 6 different pairs of pants to pair with it. For each of these pairs of pants, there are 3 different shoes to pair and so on.
Therefore, there are [tex]5\cdot 6\cdot 3\cdot 9=\boxed{810}[/tex] combinations you can make.
Convert 333 to base three.
Answer:
110100
Step-by-step explanation:
The employees of a firm that manufactures insulation are being tested for indications of asbestos in their lungs. The firm is requested to send three employees who have positive indications of asbestos to a medical center for further testing. If 40% of the employees have positive indications of asbestos in their lungs, find the probability that fifteen employees must be tested in order to find three positives. (Round your answer to three decimal places.)
Answer:
0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.
Step-by-step explanation:
For each employee, there are only two possible outcomes. Either they test positive, or they do not. The probability of an employee testing positive is independent of any other employee, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
40% of the employees have positive indications of asbestos in their lungs
This means that [tex]p = 0.4[/tex]
Find the probability that fifteen employees must be tested in order to find three positives.
2 during the first 14(given by P(X = 2) when n = 14).
The 15th is positive, with 0.4 probability. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{14,2}.(0.4)^{2}.(0.6)^{12} = 0.0317[/tex]
0.0317*0.4 = 0.013.
0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.
Please help to find this answer
Answer:
53.24 in
Step-by-step explanation:
sin(theta) = perpendicular/hypotenuse
sin(33)=29/hypotenuse
hypotenuse=29/sin(33)=53.24 in
Find the distance between the points (–2, –6) and (0, 5).
Answer:
5√5
Step-by-step explanation:
Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).
Then draw the graph of g(x).
1. g(x) = f(x + 1)
2. g(x) = f(x) - 2
Please help i also need to graph
9514 1404 393
Answer:
left 1 unitdown 2 unitsStep-by-step explanation:
The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.
1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)
__
2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)
X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b?
a perfect square trinomial, (x + y)² = x² + 2xy + y²
so, if we have the x of the bx, what is left is the b
the expression would have to be (x + 7)², since we have the 49 and the x²
so, what's left: x² + 14x + 49,
b = 14
hope it helps :)
Mr. Berber owns a $20,000 government bond that pays interest at an annual rate of 8%. Which expression below shows how many dollars he will receive as a quarterly interest payment?
Answer: (2)
Step-by-step explanation:
His yearly interest amount would be 20000(0.08).
His quarterly interest amount would be [tex]\frac{20000(0.08)}{4}[/tex], since one year has 4 quarters.
The distance, y, in miles, traveled by a car in a certain amount of time, x, in hours, is shown in the graph below:
A graph titled Motion of Car is shown with Time in hours labeled on x-axis and Distance from Starting Point in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, and the scale on the y-axis shows the numbers 0, 14, 28, 42, 56, 70, 84. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 3, 42. The second straight line joins 3,42 and 4,42 and the third straight line joins ordered pair 4,42 with the ordered pair 5,56.
Which of the following best describes the motion of the car shown?
It travels for 2 hours, then stops for 1 hour, and finally travels again for 5 hours.
It travels for 3 hours, then stops for 1 hour, and finally travels again for 1 hour.
It travels for 3 hours, then stops for 4 hours, and finally travels again for 5 hours.
It travels for 2 hours, then stops for 2 hours, and finally travels again for 1 hour.
Answer:
The last choice
Step-by-step explanation:
:)
The entire graph of the function g is shown in the figure below.
Write the domain and range of g as intervals or unions of intervals.
Step-by-step explanation:
here's the answer to your question
Which of the following numbers is rational? Assume that the decimal patterns continue.
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Answer:
(c) √49
(d) 2.544544...(3-digit repeat)
Step-by-step explanation:
Square roots of perfect squares are rational, as are repeating decimals.
Question 2 of 25
Which of the following is an equation of a line parallel to the equation
y = 4x + 1?
O A. y=1x-2
O B. y=-x-2
O C. y=-4x-2
O D. y = 4x - 2
DOSUBMIT
Answer:
y - 1 = 4x - 20.
The slope of the line y = 4x +1 is the coefficient of x, so the slope is 4. Parallel lines have the same slope, so the slope of the "other" line is also 4. Using the point-slope form of a line, the equation of the line in question is: y - 1 = 4(x - 5). Distributing 4, we get y - 1 = 4x - 20. i dont know correct me if im wrong
The profit (in thousands of dollars) of a company is given by P(x) = -8x2 + 32x + 14.
Find the maximum profit of the company.
O a. 40 thousand dollars
O b. 45 thousand dollars
O c. 46 thousand dollars
Answer:
C
Step-by-step explanation:
The profit (in thousands of dollars) of a company is given by the function:
[tex]\displaystyle P(x) = -8x^2+32x+14[/tex]
And we want to find the maximum profit of the company.
Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex. Recall that the vertex of a quadratic is given by:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
Find the x-coordinate of the vertex. In this case, a = -8, b = 32, and c = 14. Hence:
[tex]\displaystyle x=-\frac{(32)}{2(-8)}=\frac{32}{16}=2[/tex]
To find the maximum profit, substitute this value back into the function. Hence:
[tex]\displaystyle P(2) = -8(2)^2+32(2) + 14 = 46[/tex]
Therefore, the maximum profit of the company is 46 thousand dollars.
Our answer is C.
14) The height, h metres, of a ball projected directly upwards from the ground can be modelled by h = 56t - 71, where t is the time in seconds after it leaves the ground. a) Find the height of the ball 3.5 seconds after it leaves the ground. b) At what time will the ball strike the ground again? c) When will the ball be 49 m above the ground? Briefly explain why there are two possible answers.
