Answer:
- 2
Step-by-step explanation:
The average rate of change of h(x) in the closed interval [a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [a, b ] = [1, 8 ], thus
f(b) = f(8) = - 8² + 7(8) + 14 = - 64 + 56 + 14 = 6
f(a) = f(1) = - 1² + 7(1) + 14 = - 1 + 7 + 14 = 20
average rate of change = [tex]\frac{6-20}{8-1}[/tex] = [tex]\frac{-14}{7}[/tex] = - 2
Complete the factorization of 3r? – 10x + 8.
Carter made a scale drawing of a house and its lot. In real life, the backyard is 63 feet long. It is
21 inches long in the drawing. What scale did Carter use for the drawing?
1 inch :
feet
Answer: what is the question??
Step-by-step explanation:
In the figure above, AB is tangent to the circle with center o at point A.
If AOB has a measure of 68 degrees, what is the measure, in degrees, of ABO?
Given:
Given that O is the center of the circle.
AB is tangent to the circle.
The measure of ∠AOB is 68° and we know that the tangent meets the circle at 90°
We need to determine the measure of ∠ABO.
Measure of ∠ABO:
The measure of ∠ABO can be determined using the triangle sum property.
Applying the property, we have;
[tex]\angle ABO+\angle BAO+\angle AOB=180^{\circ}[/tex]
Substituting the values, we get;
[tex]\angle ABO+90^{\circ}+68^{\circ}=180^{\circ}[/tex]
Simplifying, we get;
[tex]\angle ABO+158^{\circ}=180^{\circ}[/tex]
[tex]\angle ABO=22^{\circ}[/tex]
Thus, the measure of ∠ABO is 22°
3a + b = 7
and
6x + 8y = 40
Show that 9a + 3b has a greater value than 3x + 4y
ANYONE HELP PLS
Answer:
3a + b = 7
6x + 8y = 40
9a + 3b is 3*(3a + b) or 7*3 = 21
3x + 4y is (6x + 8y) /3 = 40 / 3 ≅ 13.3
So now we know that 9a + 3b = 21 and 3x + 4y = 13.3 which means that it is greater because 21 > 13.3
If the diameter of the semicircle is 1.7 centimeters, what is the circumference of the semicircle?
To solve this you need to use this formula: 1/2Pi x D
So we can multiply 0.5 x 3.14 x 1.7
Your answer is 2.669
If r = 5 units and x = 8 units, then what is the volume of the cylinder shown above?
A.
200 cubic units
B.
40 cubic units
C.
800 cubic units
D.
130 cubic units
Answer: the answer is 200
Step-by-step explanation:
67/5 as a fraction in simplest form
Answer:
[tex] = 13 \frac{2}{5} [/tex]
Step-by-step explanation:
[tex] \: \: \: \: \: \: 13\\ 5 \sqrt{67} \\ \frac{ \: \: - 65}{ \: \: \: \: \: 02} \\ \\ \\ = 13 \frac{2}{5} [/tex]
Find the difference.
(6x +9) - (7x+1) =
Answer:-x+8
Step-by-step explanation:
So in this case we have to combine alike variables for this question.
(6x+9)-(7x+1)
-9 -9
6x-7x+-8
We had to isolate in this case thats why both alike terms were getting subtracted by 9.
Then we just combining 6x-7x since they are alike terms.
-1x+8
-1x and -x are the same thing but if you want to make it more complex, the real answer is -x+8
(I hope you find this helpful ;w;)
Answer:
-x+8
Step-by-step explanation:
What is the solution system y=2/3x-2 y=-x+3
Answer:
x = 3 , y = 0
Step-by-step explanation:
Solve the following system:
{y = (2 x)/3 - 2 | (equation 1)
y = 3 - x | (equation 2)
Express the system in standard form:
{-(2 x)/3 + y = -2 | (equation 1)
x + y = 3 | (equation 2)
Swap equation 1 with equation 2:
{x + y = 3 | (equation 1)
-(2 x)/3 + y = -2 | (equation 2)
Add 2/3 × (equation 1) to equation 2:
{x + y = 3 | (equation 1)
0 x+(5 y)/3 = 0 | (equation 2)
Multiply equation 2 by 3/5:
{x + y = 3 | (equation 1)
0 x+y = 0 | (equation 2)
Subtract equation 2 from equation 1:
{x+0 y = 3 | (equation 1)
0 x+y = 0 | (equation 2)
Collect results:
Answer: {x = 3 , y = 0
To solve the given system of equations, we can use the method of substitution. After obtaining the value of x, we can substitute it back into one of the original equations to solve for y. The solution to the system is x = 3 and y = 0.
Explanation:The given system of equations is:
y = \frac{2}{3}x - 2
y = -x + 3
To solve this system, we can use the method of substitution. We can rearrange the second equation to solve for y:
y = -x + 3
Now, substitute this value of y into the first equation:
\frac{2}{3}x - 2 = -x + 3
Add x to both sides:
\frac{2}{3}x + x - 2 = 3
Multiply both sides by 3 to eliminate the fraction:
2x + 3x - 6 = 9
Combine like terms:
5x - 6 = 9
Add 6 to both sides:
5x = 15
Divide both sides by 5:
x = 3
Now, substitute the value of x back into one of the original equations to solve for y:
y = -x + 3
y = -3 + 3
y = 0
Therefore, the solution to the system of equations is x = 3 and y = 0.
Learn more about Systems of Equations here:https://brainly.com/question/35467992
#SPJ3
EXPERIMENTAL
FISH
FREQUENCY
EXPERIMENTAL
PROBABILITY
pink salmon
yellowfin tuna
bluegill
Total
11
16
23
50
%
?
100%
0
E to search
Answer:
fish. pink salmon. 50. i like fish btw
Step-by-step explanation:
Experimental probabilities: Pink Salmon 22%, Yellowfin Tuna 32%, Bluegill 46%. Total probability equals 100%.
To find the experimental probability of each type of fish, we first need to calculate the percentage of each type of fish out of the total number of fish caught.
Experimental Probability ($P$) is given by:
[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \times 100 \][/tex]
Let's calculate:
1. Pink Salmon:
[tex]\[ P(\text{Pink Salmon}) = \frac{11}{50} \times 100\% = \frac{11}{50} \times 100\% = 22\% \][/tex]
2. Yellowfin Tuna:
[tex]\[ P(\text{Yellowfin Tuna}) = \frac{16}{50} \times 100\% = \frac{16}{50} \times 100\% = 32\% \][/tex]
3. Bluegill:
[tex]\[ P(\text{Bluegill}) = \frac{23}{50} \times 100\% = \frac{23}{50} \times 100\% = 46\% \][/tex]
Now, let's check if the total probability sums up to 100%:
[tex]\[ 22\% + 32\% + 46\% = 100\% \][/tex]
Yes, it does.
So, the experimental probability of catching pink salmon is [tex]\(22\%\),[/tex]yellowfin tuna is[tex]\(32\%\)[/tex], and bluegill is [tex]\(46\%\).[/tex]
Complete question;
What is the probability of selecting each type of fish in an experimental study when the total frequency of fish sampled is 50? The types of fish sampled are pink salmon, yellowfin tuna, and bluegill. The frequencies of each fish type are 11, 16, and 23 respectively.
Jeff has $20. He spent 1/8 of his money on lunch and 2/5 of his money at the movies. How much money does Jeff have left?
A. $5.50
B. $7.00
C. $8.25
D. $9.50
Answer:
D. $9.50
Step-by-step explanation:
In total, Jeff spends 21/40 of his money. (1/8+2/5=21/40)
He has 19/40 left.
19/40*20=380/40=9.5
First, let's put 2/5 and 1/8 into similar fractions, in that they have the same denominator.
2/5 = 16/40
1/8 = 5/40
Then, we'll add the fractions together.
16/40 + 5/40 = 21/40
So, Jeff spent 21/40 of his money. We can set up a proportion to find the amount that Jeff spent.
x/20 = 21/40
420 = 40x
x = 10.50
Finally, we'll subtract the amount that Jeff spent from the original amount.
20 - 10.50 = 9.50
Jeff has D. $9.50 left.
Hope this helps!! :)
Please please answer this correctly I have to finish this today as soon as possible
Answer:
Step-by-step explanation:
Look at where -2 is on the x-axis (the left side of the horizontal line), and go another half a box in, that is -2.5. But then go down one box from there, and plot the point. that is (-2.5,-1).
Next go half a box to the right and two boxes up, and plot your point there. that is (.5,2).
Help two helpless triangles?
Answer:
see below
Step-by-step explanation:
Angle ACE = DCE since they are vertical angles
Angle A = Angle E parallel lines cut by a transversal form congruent alternate interior angles
Angle B = Angle D parallel lines cut by a transversal form congruent alternate interior angles
When all three angles are equal, the triangles are similar.
We can use ratios to find DE
DE CE
------- = ----------
AB AC
DE 8
------- = ----------
12 10
Using cross products
10 DE = 8*12
10 DE = 96
Divide by 10
DE = 9.6
Answer:
1) they are similar by AAA postulate
2) 9.6 cm
Explanation:
Triangles CAB and CED are similar
because:
1) both have the same angle C
(vertically opposite angles)
2) Angle A = Angle E
(alternate angles)
3) Angle B = Angle D
(alternate angles)
CA/CE = AB/ED
10/8 = 12/DE
DE = 12 × 8/10
DE = 9.6 cm
A study of 420,076 cell phone users found that 131 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such
cancer was found to be 0.0224% for those not using cellphones. Complete parts (a) and (b)
a. Use the sample data to construct a 95 i dence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system
%
(Round to three decimal places as needed)
Answer:
a) 95% Confidence interval = (0.026%, 0.037%) to 3 d.p
b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = (131/420076) = 0.0003118483 = 0.0312%
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 95% confidence interval for sample size of 420,076 is obtained from the z-tables because the sample size is large enough for the properties of the sample to approximate the population properties.
Critical value = 1.960 (from the z-tables)
Standard error = σₓ = √[p(1-p)/n]
n = sample size = 420,076
σₓ = √(0.0003118×0.999688/420076) = 0.0000272421 = 0.0000272
95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.000312 ± (1.96 × 0.0000272)
CI = 0.000312 ± 0.0000534
95% CI = (0.0002586055, 0.0003653945)
95% Confidence interval = (0.000259, 0.000365)
95% Confidence interval = (0.0259%, 0.0365%) = (0.026%, 0.037%) to 3 d.p
b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.
Hope this Helps!!!
Tree is 4.5 feet tall plum tree is 3/4 foot taller . How y’all is the plum tree
Answer:
7.875 (not sure what your unit is but include it here)
Step-by-step explanation:
3/4 of 4.5 is 3.375
3.375+4.5=7.875
You start a search for a buried object by marking the center of a field as (0, 0), with
coordinates giving distances in yards. Coordinates to the north or east are positive, and
coordinates to the south or west are negative. You find nothing at (–10, 6), so you try a likely
looking spot 3 yards to the east and 12 yards to the south of the first spot. What are the
coordinates of the second spot?
(–7, –6)
(12, –6)
(–13, –9)
(5, –3)
Answer:
(-7,-6)
Step-by-step explanation:
-10 + 3 = -7
6 - 12 = -6
(-7,-6)
The following data points represent the yearly salaries of high school cheerleading coaches in Dakota county (in thousands of dollars). 41 38 36 57 43
Answer:
5.6 thousand
Step-by-step explanation:
To find the mean absolute deviation (MAD), first find the mean (or average).
μ = (41 + 38 + 36 + 57 + 43) / 5
μ = 43
Next, subtract the mean from each value and take the absolute value.
|41 − 43| = 2
|38 − 43| = 5
|36 − 43| = 7
|57 − 43| = 14
|43 − 43| = 0
Sum the results and divide by the number of animals.
MAD = (2 + 5 + 7 + 14 + 0) / 5
MAD = 5.6
Answer:
43 thousand dollars
Which face of the net will be the shaded side of the prism when the net is folded.
A
B
C
D
Answer:
A
Step-by-step explanation:
A: will be the connect with 2 sides of hypotenuse of the triangle
A graph has time (years) on the x-axis and height (inches) on the y-axis. A line goes through points (2, 3) and (4, 6).
The graph shows a linear relationship between the height and years of a plant’s growth. Find the rate of change. Select all that apply.
The rate of change of a linear function is always the same.
The rate of change of a linear function increases as the input increases.
The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.
The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.
Answer:
A, C, and D
Step-by-step explanation:
The rate of change will simply be the slope of the line, which we can find by taking the change in y and dividing that by the change in x:
slope = [tex]\frac{6-3}{4-2} =\frac{3}{2}[/tex]
Thus, the slope is 3/2 = 1.5.
Since the slope remains constant throughout the graph, we know that A is correct. In addition because the points 0, 2, 4, and 6 are on the graph, the rate of change between any of the two points will still be the constant 1.5, making C and D correct as well.
So, we can choose A, C, and D.
Hope this helps!
Answer:
The rate of change of a linear function is always the same.
The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.
The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.
Step-by-step explanation:
Slope = rate = (6 - 3)/(4 - 2) = 3/2
Slope of a straight line is constant hence the rate of change is also constant
Please help. Simplify cos(−0)cot(−0) / csc(0)
Answer:
C) cos²(theta)
Step-by-step explanation:
csc(X) = 1/sin(X)
cos(-X) = cos(X)
tan(-X) = -tan(X)
cot(-X) = -1/tan(X) = -cos(X)/sin(X)
[cos(X) × -cos(X)/sin(X)] ÷ -1/sin(X)
-cos²(X)/sin(X) × -sin(X)
cos²(X)
8 into 6482 what is the placement value
Answer:
It is 80.
Step-by-step explanation:
It's pretty simple-> Thousands, Hundreds, Tens, Ones.
Answer:
The tens place
Step-by-step explanation:
place values:
6000
400
80
2
Find the weight of the metal gate. I need help finding another to prove it weighs 42.5kl as you will see it is incomplete.
Answer:
150 kg
Step-by-step explanation:
The diagonal Piece: √5²+12² = 13
6 pieces: 5, 12, 5, 12, 13, 13
Total length: 2 x(5 + 12 + 13) = 60
Total weight: 60 x 2.5 = 150 kg
Answer:
150 kg
Step-by-step explanation:
The length of the diagonal:
sqrt(12² + 5²)
sqrt(169)
13
Total length:
2(13 + 12 + 5)
2(30)
60m
Mass;
60 × 2.5
150 kg
A translation moves point V(-2, 3) to V-2,7). Which are true statements about the translation?
1. The point moves two units left and four units up.
2.The transformation rule is (x,y) = (x+0.7+4).
3.The transformation is a vertical translation.
4.The image is four units to the left of the pre-image.
5.The translation can be described as (x, y) = (x-2, Y+7).
Answer:
2. The transformation rule is (x, y) -> (x + 0, y + 4).
Step-by-step explanation:
The true statements about the translation are:
2. The transformation rule is (x,y) = (x+0.7+4).
3. The transformation is a vertical translation.
The vertices are given as:
V(-2, 3) to V-2,7)
From the above vertices, we have the following transformation rule
(x,y) = (x+0.7+4).
Notice that the x-coordinate remains unchanged,
This means that the transformation is a vertical translation.
Hence, the true statements about the translation are: (2) and (3)
Read more about translation at:
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What is the sign of 3x y3xy3, x, y when x>0x>0x, is greater than, 0 and y<0y<0y, is less than, 0?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Positive
(Choice B)
B
Negative
(Choice C)
C
Zero
Answer:
B ) Negative
Step-by-step explanation:
Given the expression 3xy
when x>0 and y<0
The value of the expression 3xy will be negative.
This is because the product of a positive and negative number will always be negative.
For illustration,
Let x=5>0 and y=-5<0
3xy=3(5)(-5)=-75
NOTE:
[tex]-X-=+\\-X+=-\\+X+=+[/tex]
what is the domain of f(x) = 3x/x-1?
a all real numbers
b all nonzero numbers
c all real numbers except 1
d all real nunbers except 3
Alexander is drawing a map of the Federal Triangle in Washington, D.C. The actual Federal Triangle has a base of 30 feet and height of 1200 feet. Alexander needs his drawing to fit on his paper, so he decides to make the base of his triangle 10 inches. What scale is Alexander using?
Answer:
Step-by-step explanation:
First let's figure out the scale Alexander is using by relating the base in his drawing 10 in/3000 ft = 1 in/300 ft
The scale for the drawing is 1 in:300 ft.
We know the actual Federal Triangle has a height of 1200 ft Let's use the scale to find the height of Alexander's triangle.
1200 ft times 1 in/300 ft = 4 in.
Alexander is using a scale of 1 in: 300 ft.His triangle has a height of 4 in.
If x negative squared = 16, what is the value of x squared?
A. 1/16
B. 1/4
C. 2
D. 4
E. 12
Answer:
Step-by-step explanation:
[tex]x^{-2}=16\\\\\frac{1}{x^{2}}=16\\\\[/tex]
Cross multiplication,
[tex]1=16x^{2}\\\\\frac{1}{16}=x^{2}[/tex]
Consider the two functions y=3/4x - 2 which statement is true?
a) function 1 has a greater rate of change by 1/4
The second line has a greater rate of change by 13/4.
To determine the rate of change, or slope, of the given graphed line, we employ the formula for calculating the slope between two points, expressed as:
a = (y2 - y1)/(x2 - x1)
Observing the graphed function, we identify two points, (0, -2) and (4, 0), and apply these coordinates to the slope formula
a = (0 - (-2))/(4 - 0) = 2/4 = 1/2
Having established that the slope of the first line is 1/2, we move on to the second line, which has a slope of 15/4. To find the difference in slopes, we subtract the slope of the first line from that of the second:
15/4 - 1/2 = 15/4 - 2/4 = 13/4
This calculation reveals that the second line has a greater rate of change by 13/4.
In summary, the step-by-step analysis indicates that the slope of the second line exceeds that of the first by 13/4.
The question probable may be:
Consider the two functions. Which statement is true?
A)Function 1 has a greater rate of change by 13/4
B)Function 2 has a greater rate of change by 13/4
C)Function 1 has a greater rate of change by 13/2
D)Function 2 has a greater rate of change by 13/2
(2x^2+4-5)-(-8x+2+x^2)
Answer:
x2 + 8x - 3
Step-by-step explanation:
1 . ((2x2 + 4) - 5) - (x2 - 8x + 2)
2. Factoring x2+8x-3
The first term is, x2 its coefficient is 1 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 8 .
Step 3. -3
+
1
=
-2
-1
+
3
=
2
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
So that the answer
Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.
Let k be Kevin's age and let d be Daniel's age.
Answer : Define F as fathers age and S as sons age right now.
Then now they are
(1) 3S = F
and six years ago they were
(2) 5*(S-6) = F-6
calculate 5*(S-6)
5S - 30 = F-6
Subtract left and right side by -F
Add 30 to left and right side
5S - F = 24
Put (2) 3S = F into the equation above
5S - 3S = 24
2S = 24
S = 12
insert result in (2) 3S = F
3*12 = F
36 = F
So the son is 12 years, and the father is 36 years.
"The correct system of equations to represent Kevin's and Daniel's ages is:
1. k = d + 3
2. k - 2 = 4(d - 2)
To solve for Kevin's and Daniel's current ages, we can substitute k from equation 1 into equation 2.
From equation 1:
k = d + 3
Substitute k into equation 2:
(d + 3) - 2 = 4(d - 2)
Now, simplify the equation:
d + 1 = 4d - 8
Combine like terms:
4d - d = 8 + 1
3d = 9
Divide both sides by 3 to solve for d :
d = [tex]\frac{9}{3}[/tex]
d = 3
Now that we have Daniel's age, we can find Kevin's age by substituting d back into equation 1:
k = d + 3
k = 3 + 3
k = 6
Therefore, Kevin is 6 years old and Daniel is 3 years old. The final answer is:
Kevin's age: k = 6
Daniel's age: d = 3 "