Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
Step-by-step explanation:
Step 1: Solve using the first point
(2, 28)
[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]
[tex]28 = 8a + 4b + 2c + d[/tex]
Step 2: Solve using the second point
(-1, -5)
[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]
[tex]-5 = -a + b - c + d[/tex]
Step 3: Solve using the third point
(4, 220)
[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]
[tex]220 = 64a + 16b + 4c + d[/tex]
Step 4: Solve using the fourth point
(-2, -20)
[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]
[tex]-20 = -8a + 4b - 2c + d[/tex]
Step 5: Combine the first and fourth equations
[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]
[tex]8 = 8b + 2d[/tex]
[tex]8 - 8b = 8b - 8b + 2d[/tex]
[tex](8 -8b)/2 = 2d/2[/tex]
[tex]4 - 4b = d[/tex]
Step 6: Solve for c in the second equation
[tex]-5 + 5 = -a + b - c + d + 5[/tex]
[tex]0 + c = -a + b - c + c + d + 5[/tex]
[tex]c = -a + b + d + 5[/tex]
Step 7: Substitute d with the stuff we got in step 5
[tex]c = -a + b + (4 - 4b) + 5[/tex]
[tex]c = -a + b + 4 - 4b + 5[/tex]
[tex]c = -a - 3b + 9[/tex]
Step 8: Substitute d and c into the first equation
[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]
[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]
[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]
[tex]6 / 6 = (6a - 6b) / 6[/tex]
[tex]1 + b = a - b + b[/tex]
[tex]1 + b = a[/tex]
Step 9: Substitute a, b, and c into the third equation
[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]
[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]
[tex]220 - 100 = 60b + 100 - 100[/tex]
[tex]120 / 60 = 60b / 60[/tex]
[tex]2 = b[/tex]
Step 10: Find a using b = 2
[tex]a = b + 1[/tex]
[tex]a = (2) + 1[/tex]
[tex]a = 3[/tex]
Step 11: Find c using a = 3 and b = 2
[tex]c = -a - 3b + 9[/tex]
[tex]c = -(3) - 3(2) + 9[/tex]
[tex]c = -3 - 6 + 9[/tex]
[tex]c = 0[/tex]
Step 12: Find d using b = 2
[tex]d = 4 - 4b[/tex]
[tex]d = 4 - 4(2)[/tex]
[tex]d = 4 - 8[/tex]
[tex]d = -4[/tex]
Answer: [tex]a = 3, b = 2, c = 0,d = -4[/tex]
Evaluate 6p, when p=4
Answer:
24
Step-by-step explanation:
6(4) = 24
Answer:
24
Step-by-step explanation:
What is the value of s?
units
0
5
В
8
15
S
D
Consider the triangle ABD,
Here,
AB = 5
BD = 15
AD = s
As we know,
In a triangle, the sum of lengths of two sides is greater than the third side.
So,
[tex]5 + 15 > s[/tex]
[tex]15 + s > 5[/tex]
[tex]s + 5 > 15[/tex]
Now,
To satisfy the equation, the value of s can possibly be 11, 12, 13, 14, 15, 16, 17, 18, 19
Answer: the value of s is 17 units
Step-by-step explanation: youre welcome
Find the range of the data in the box plot below.
Answer:
Range: 20
General Formulas and Concepts:
Statistics
Range - the difference between the highest and lowest pointStep-by-step explanation:
Step 1: Define
Find values from box-and-whisker plot.
Highest point recorded = 25
Lowest point recorded = 5
Step 2: Find Range
Set up: 25 - 5Subtract: 20f(x) = -5x+5. f(-2)
Answer:
f(-2)=15
Step-by-step explanation:
To find f(-2), we want to find what f(x), or y is, when x is equal to -2.
f(x)= -5x+5
Therefore, we can substitute -2 in for x.
f(-2)= -5(-2)+5
Now, solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Multiply -5 and -2
f(-2)=10+5
Add 10 and 5
f(-2)=15
Answer:
f(-2) = 15, or y = 15
Step-by-step explanation:
f(-2) = -5(-2) + 5
f(-2) = 10 + 5, a negative multiplied by a negative will be a positive !
f(-2) = 15
y = 15
Please help I will mark brainliest
Answer:
1 acute angle
2 acute angle
Step-by-step explanation:
less than 90° acute angle
more than 90° obtuse angle
90° right angle
A school in New Zealand collected data about the employment status of the mother and father in two-parent families. The two-way table of column relative frequencies below shows the data.
Father works full time Father works part time Father not working
Mother works full time
0.17
0.170, point, 17
0.14
0.140, point, 14
0.13
0.130, point, 13
Mother works part time
0.23
0.230, point, 23
0.14
0.140, point, 14
0.07
0.070, point, 07
Mother not working
0.60
0.600, point, 60
0.71
0.710, point, 71
0.80
0.800, point, 80
Column total
1.00
1.001, point, 00
1.00
1.001, point, 00
1.00
1.001, point, 00
Based on the data, which of the following statements must be true for the two-parent families at that school?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
A family where the father works part time is twice as likely as a family where the father is not working to have the mother work part time.
(Choice B)
It is most common for neither parent to be working.
(Choice C)
C
Families where the father works full time are more likely to have the mother working full time than part time.
(Choice D)
D
There are twice as many families where the mother works full time and the father works part time as families where the mother works part time and the father doesn't work.
Answer:A
Step-by-step explanation: 14% of the mothers work part-time in families where the father works part-time while 7% of the mothers work part-time in families where the father is not working.
Probabilities are used to determine how likely or unlikely an event is. From the 2-column table, it is twice as likely to get a family where the father and the mother work part-time than a family where the father doesn't work, and the mother works part-time.
We use the following representation:
[tex]FF \to[/tex] Father works full-time
[tex]FP \to[/tex] Father works part-time
[tex]FW \to[/tex] Father not working
[tex]MF \to[/tex] Mother works full-time
[tex]MP \to[/tex] Mother works part-time
[tex]MW \to[/tex] Mother not working
Next, we test each of the 4 options, till one of the options is true (see attachment)
Choice A:
The claim in choice A is that:
[tex]P(FP\ and\ MP) = 2 \times P(FW\ and\ MP)[/tex]
From the given table, we have:
[tex]P(FP\ and\ MP) = 0.14[/tex] ---- father works part-time and mother works part-time
[tex]P(FW\ and\ MP) =0.07[/tex] ---- father not working and mother works part-time
Put the above values in the following equation
[tex]P(FP\ and\ MP) = 2 \times P(FW\ and\ MP)[/tex]
[tex]0.14 = 2 \times 0.07[/tex]
[tex]0.14 = 0.14[/tex]
The above equation is true.
Hence, choice (A) is true
Read more about probabilities at:
https://brainly.com/question/24297863
Eric, Cam, and Brooke are playing a game of mini golf on a computer. The computer program for the game stores
objects in terms of x and y coordinates. All coordinate values are in meters.
The players are shooting at the hole, which is located at (3,2). After hitting their initial shots, Eric's golf ball is at
(-6,6), Cam's golf ball is at (8,-6), and Brooke's golf ball is at (10,8).
If the player whose ball is farthest from the hole should shoot next, which player should shoot next?
Answer:
Eric
Step-by-step explanation:
First, we determine the distance of each player to the hole using the distance formula.
Given points [tex](x_1,y_1)$ and (x_2,y_2)[/tex]
Distance[tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Eric
The hole is at (3,2)
Eric's golf ball is at point (-6,6)
Distance=[tex]\sqrt{(-6-3)^2+(6-2)^2}[/tex]
[tex]=\sqrt{(-9)^2+(4)^2}\\=\sqrt{97} \\\approx 9.85[/tex]
Cam
The hole is at (3,2)
Cam's golf ball is at point (8,-6)
Distance=[tex]\sqrt{(8-3)^2+(-6-2)^2}[/tex]
[tex]=\sqrt{(5)^2+(-8)^2}\\=\sqrt{89} \approx9.43[/tex]
Brooke
The hole is at (3,2)
Brooke's golf ball is at point (10,8)
[tex]Distance=\sqrt{(10-3)^2+(8-2)^2}\\=\sqrt{(7)^2+(6)^2}\\=\sqrt{85} \approx 9.22[/tex]
Since Eric's ball is the farthest from the hole, Eric should shoot next.
Answer: Erick
Step-by-step explanation: 9.85
3) A box of chocolates contains four milk
chocolates and four dark chocolates. You
randomly pick a chocolate and eat it.
Then you randomly pick another piece.
The first piece is milk chocolate and the
second piece is dark chocolate.
Are the events independent or dependent?
What is the probability?
Answer:
dependent and 2/7
Step-by-step explanation:
dependent because you didn't replace it.
1/2 times 4/7 which is 4/14 which equals to 2/7
1. Write yes or no if its a proportion
2.Write yes or no if its a proportion
3. Equation
Answer:
1. yes
2. yes
3. (3,60)
hi what is the answer
Answer:
A = 176.63 cm²
Step-by-step explanation:
Area of circle = π r ²
A = (3.14)(7.5)²
A = (3.14)(56.25)
A = 176.63 cm²
Answer:
Area of circle = pi x radius^2 = 3.142 x 7.5^2 = 176.74 (cm2)
Hope this helps!
:)
What is the constant rate of change in the function y=5x?
1/5
x
5
1
Answer:
5
Step-by-step explanation:
The rate of change is the slope
y = 5x
The slope is the constant in front of the x
The constant rate of change is 5
What do the stage directions at the end of the excerpt indicate?
Answer:
The stage direction at the end of an excerpt are used to provide information about how the characters should move or speak on stage.
Answer:
The stage direction at the end of an excerpt are used to provide information about how the characters should move or speak on stage.
Step-by-step explanation:
Can I please get help with this math problem?
what is 50300000 in standard form
Answer:
the answer is attached in the picture
Question 15
2 pts
The daily caloric intake for a group of women follows a normal distribution with a mean of
1,750 calories and a standard deviation of 200 calories. What is the z-score for a woman
who had a daily intake of 2,100 calories?
2,091
-1.75
1.75
1.09
Question 16
2 pts
What is it called when you get a positive test result for a disease that you do not have?
False Negative
Margin of Error
Accuracy
True Positive
False Positive
Answer:
1. Z = 1.75
2. False Positive
Step-by-step explanation:
1. mean = 1750 calories
standard deviation, sd = 200 calories
value of interest, x = 2,100
z-score is computed as follows:
Z = (x - mean)/sd
Z = (2100 - 1750)/200
Z = 1.75
2. A false positive happens, when a negative case is detected as a positive case
show work please. need asap.
Answer:
129 = QRX
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
49+80 = QRX
129 = QRX
Answer:
129°
Step-by-step explanation:
Exterior angle = sum of interior angles
Angle QRX = 49 + 80
= 129°
If Marc ran 10 miles in 3 hours, how far can he run in 6 hours?
Answer: 20 miles
Step-by-step explanation: if he runs 10 miles in 3 hours then double the amount of 10 which is 20 because 3 multiplied by 2 equals 6
I NEED HELP!
Line 9 and 10
To calculate your taxable income, subtract the sum of lines 8 and 9 from line 7.
Can I get an example of systems of equations that represent the solution of this situation below? Thank you! ^ ^
"1 taco and 1 burrito costs $11. 10 tacos and 5 burritos cost $80. How much is the cost of one burrito?" (x = the cost of a taco, and y = the cost of a burrito)
Answer:
1x+ 1y =11
10x + 5y = 80
x = the cost of a taco = $5
y = the cost of a burrito = $6
Step-by-step explanation:
x = the cost of a taco
y = the cost of a burrito
1x+ 1y =11
10x + 5y = 80
rearange 1st equation as y = 11 -x and plug in into the 2nd one for y:
10x + 5( 11-x) = 80 distribute left side
10x + 55 - 5x = 80 combine like terms
10x - 5x = 5x
5x + 55 = 80 subtract 55 from both sides
5x = 80 - 55
5x = 25 divide by 5
x = 5
plug in for y in 1st equation y = 11--x =11-5 = 6
Help me find the MAD volume please
How many sundaes are there?
Answer:
2
Step-by-step explanation:
8+12+4+8 = 32
32/4 = 8
8-8 = 0
12-8 = 4
8-4 = 4
8-8 = 0
4+4+0+0 = 8
8/4 = 2
Which of the following properly describe “slope”?
Answer:
#3 1/2
Step-by-step explanation:
if you start where the line and the boxes in the graph line up like at (0,-2) and then you go up 1 and right 2 the line will be there again line up with the boxes and since slope is rise/run it is 1/2
When multiplying or dividing a negative by a negative what will the result be
Answer:
A positive number
Step-by-step explanation:
The image of a triangle after it has been dilated with a center of dilation at the origin has vertices at A prime(12, –6), B prime(–24, –12), and C prime. If the pre-image of B prime, point B, has coordinates of (–18, –9) and the pre-image of C prime, point C, has coordinates of (–13.5, 18), which statements are true? Check all that apply. The coordinates of C prime are (27, 18). The coordinates of C prime are (–18, 24). The scale factor is 1 and one-third. The scale factor is 1 and one-fifth. The scale factor is Three-fourths. The coordinates of A are (16, –8). The coordinates of A are (9, –4.5).
Answer:
C is (-18, 24)
Scale factor --> 1 1/3
A is (9, - 4 1/2) *4 1/2 is also 4.5
Brainliest please, I need a few more :D
The true statement are; The coordinates of C prime are (–18, 24). The scale factor is 1 1/3 . The coordinates of A are (9, –4.5).
How to find if a pair of figure is not dilated version of each other?Dilation of a figure will leave its sides get scaled (multiplied) by same number.
Thus, suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.
At image B (-24, -12) and pre image B (-18, -9),
we can work out the scale factor by (-24/-18) and (-12/-9) both equal 4/3
Using the scale factor to go from the pre image to the image,
We can find C coordinate by pre image C by the scale factor.
C is (-13.5 x 4/3) and (18 x 4/3)
C is (-18, 24)
So, The scale factor is 4/3, which is the mixed numeral of 1 1/3.
To find the pre image of point A;
A is (12/(4/3)) and (-6/(4/3))
A is (9, - 4 1/2)
Hence, the true statement are;
The coordinates of C prime are (–18, 24).
The scale factor is 1 1/3 .
The coordinates of A are (9, –4.5).
Learn more about dilation here:
https://brainly.com/question/27212783
#SPJ5
find the area of the composite figure
Answer:
Quickly learn how to find the Area of Composite Figures in today's geometry lesson. With 19 worked examples, you'll have everything you need ...
Step-by-step explanation:
Percentages less than 100% definition
Answer:
fractions
Step-by-step explanation:
Answer:
A number or ratio expressed as a fraction of 100
Step-by-step explanation:
Use outside of percentages but reused under 100 when explained.
Steepness of a hill or gradient of a line = rise/run x 100
On a graph the numbers go from 0 for flat, to 100% at 45 degrees, to infinity as it approaches vertical.
Percentage is Tangent of a circle as where it meets it angle it always is intercepted by the circumference or new angle and becomes less than 180 as it forms a leg of a shape, or a side and 1% represents 100 x 0.01000033334% in Radians as another example. we multiply by 100 and get 1 Rad or a 180 degree line. Broadness of usefulness in percentage is the ratio so 1% of a radian can be the decimal above, and 100% of 1 rad = 180/pi =57.2957 We find a semi-circle has an arc length of pi*r and also that it is 180 degrees. From that you can conclude that the number of degrees in a radian is 180/pi and shows 50% of the circle but 100% of 1 radian.
which of the following is equivalent to the expression below?
(a²-2b²+3)-(4b²+5)+(3a²+4)
A: 4a²-6b²+12
B: 4a²-6b²+2
C: 4a²+2b²+2
D:4a²+2b²+12
Answer:
4a^2−6b^2+2 so B
Step-by-step explanation:
can someone help me find the area please?
Answer:
The area would be 48 m.
Step-by-step explanation:
PLEASE HELP
Results of a blood test are normally distributed with a mean of 6.2 and a standard deviation of 1.5. What is the probability that a patient has a blood test result less than or equal to 8.3?
Answer:
91.92%
Step-by-step explanation:
Given that:
Mean (μ) = 6.2, standard deviation (σ) = 1.5
Z score is a measure in statistics to determine the relationship of a measured value with the mean. It is given by the equation:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
To calculate the probability that a patient has a blood test result less than or equal to 8.3, we need to calculate the z score of 8.3
For x = 8.3, the z score is:
[tex]z=\frac{x-\mu}{\sigma}=\frac{8.3-6.2}{1.5} =1.4[/tex]
From the probability distribution table:
P( x ≤ 8.3) = P(z < 1.4) = 0.9192 = 91.92%
HALF LIFE The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning,
how many grams would be left after 7.2 minutes has elapsed?
A: 50.0 grams
B: 100.0 grams
C: 8.5 grams
D: 12.5 grams
Answer:
7.2 / 2.4 = 3 half-lives
(1/2)3 = 0.125 (the amount remaining after 3 half-lives)
100.0 g x 0.125 = 12.5 g remaining
Hope this Helped! :)
Find the area of a circle with a diameter of 4.
Either enter an exact answer in terms of or use 3.14 for i and enter your answer as a decimal.
Answer:
12.57
Step-by-step explanation:
