Using the limit definition of the derivative, you have
[tex]\displaystyle f'(-5) = \lim_{x\to-5} \frac{f(x) - f(-5)}{x - (-5)} = \lim_{x\to-5} \frac{(2x^2+4x+7) - 37}{x + 5}[/tex]
Simplify the numerator:
(2x ² + 4x + 7) - 37 = 2x ² + 4x - 30
… = 2 (x ² + 2x - 15)
… = 2 (x + 5) (x - 3)
Then
[tex]\displaystyle f'(-5) = \lim_{x\to-5}\frac{2(x+5)(x-3)}{x+5} = \lim_{x\to-5} 2(x-3) = \boxed{-16}[/tex]
• • •
For your second question in the comments, if f(x) = -2x ² + 3x - 7, then by the definition of the derivative, you have
[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0}\frac{(-2(x+h)^2+3(x+h)-7) - (-2x^2 + 3x - 7)}h[/tex]
Simplify the numerator:
(-2 (x + h)² + 3 (x + h) - 7) - (-2x ² + 3x - 7)
… = (-2x ² - 4xh - 2h ² + 3x + 3h - 7) - (-2x ² + 3x - 7)
… = -4xh - 2h ² + 3h
Now compute the limit:
[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{-4xh-2h^2+3h}h = \lim_{h\to0}(-4x-2h+3) = \boxed{-4x+3}[/tex]
A rectangular fish tank is 2m long, 1m wide and 1m deep. How many litres of water will it hold?
Answer:
2000 litres
Step-by-step explanation:
find the volume
v =2m×1m×1 m
= 2 m3
1m3 =1000litres
2m3=????
cross multiply
2m3 ×1000litres
1m3
Ans = 2000litres
FIND THE PERIMETER OF THE TRAPEZOID HELPPP MEEEE
Answer:
18.9
Step-by-step explanation:
hope this helps have a great day
I NEED THIS ASAP. What is m
Answer:
The measure of ∠DFE is 67°.
Step-by-step explanation:
Angle GFE is a straight angle, meaning that its measure is 180°, per se.
180 - 113 = m of ∠DFE
180 - 113 = 67
5. Laney is 4 feet 8 inches tall. There are 2.54
centimeters in 1 inch. What is Laney's height in
centimeters?
A. 22.05
B. 96.8
C. 142.24
O D. 160.32
will mark brainlest
Find the area of the polygon in square units.
Answer:
I wanna say 18 but I'm not to sure
Help this type of work confuses me
Answer/Step-by-step explanation:
Given:
-x + 3x + 1 + 4(x + 2) = 54
To solve, first open the bracket by applying the distributive property. Multiply every term you have in the bracket by 4
-x + 3x + 1 + 4x + 8 = 54
Add like terms together
6x + 9 = 54
Subtract 9 from each side
6x = 54 - 9
6x = 45
Divide both sides by 6
x = 45/6
x = 7.5
Please help me PLEASE and NO LINKS OR YOU WILL BE REPORTED. I need help choosing the right statements also the line plot I chose is correct so you can use it to help you.
The first one is “The greatest length is 2 inches more than the least length.”
The second is “Less than half the lures are at least 3 inches long.”
The third is “The number of lures greater than 2 1/2 inches long is less than the number of lures less than 2 1/2 inches
The fourth is “The greatest length is 2 inches.”
The fifth is “The number of lures greater than 2 1/2 inches long is equal to the number of lures less than 2 1/2.” Please help me
Answer:
why no links? also I think the answer is 5 but I'm just guessing
Answer:
g sa Bshsixuzsh- shshshakka
In a math class with 19 students, a test was given the same day that an assignment was due. There were 10 students who passed the test and 11 students who completed the assignment. There were 6 students who failed the test and also did not complete the assignment. What is the probability that a student chosen randomly from the class passed the test and completed the homework?
Answer:
8/19
Step-by-step explanation:
The probability that a student is chosen randomly from the class passed the test and completed the homework will be 0.1637.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
In a math class with 19 students, a test was given the same day that an assignment was due.
There were 10 students who passed the test and 11 students who completed the assignment.
There were 6 students who failed the test and also did not complete the assignment.
Then the probability that a student is chosen randomly from the class passed the test and completed the homework will be
The number of the student who has done at least one assignment or passed the test is 19 - 6 = 13
n(A) = passes student
n(B) = given assignment
Then we have
[tex]\rm n(A \cap B) = n(A) + n(B) - n(A \cup B) \\\\n(A \cap B) = 10 + 11 - 13\\\\n(A \cap B) = 8[/tex]
Then the probability will be
[tex]\rm P = \dfrac{^8C_2}{^{19}C_2}\\\\P = \dfrac{28}{171}\\\\P = 0.1637[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
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A company says its premium mixture of nuts contains % Brazil nuts, % cashews, % almonds, and % hazelnuts, and the rest are peanuts. You buy a large can and separate the various kinds of nuts. Upon weighing them, you find there are grams of Brazil nuts, grams of cashews, grams of almonds, grams of hazelnuts, and grams of peanuts. You wonder whether your mix is significantly different from what the company advertises.
1) Explain why the chi-square goodness-of-fit test is not an appropriate way to find out.
A) The chi-square goodness-of-fit test can only be used on counts, weights are quantitative, not counts.
B) The chi-square goodness-of-fit test can only be used on quantitative variable, weights are counts, not quantitative variables.
C) The expected values are percentages, and the actual values are not. Therefore the ch-square goodness-of-fit test cannot be used.
D) The chi-square goodness-of-fit test cannot be use to test this kind of claim
2) What might you do instead of weighing the nuts in order to use a X2 test?
A) There is no way of performing a test without using weight.
B) Count the number of each kind of nut, assuming the company's percentages are based on counts rather than weights.
C) Find the volume of each kind of nut, assuming the company's percentages are based on volume.
Answer:
A) The chi-square goodness-of-fit test can only be used on counts, weights are quantitative, not counts.
B) Count the number of each kind of nut, assuming the company's percentages are based on counts rather than weights.
Step-by-step explanation:
The Test of Goodnes for fit is based on the property that the χ² test is applicable when the cell probabilities depend on unknown parameters, provided that the unknown parameters are replaced with their estimates and provided that the one degree of freedom is deducted from each parameter estimated.
1) So if the estimates ( counts) are missing the test is not applicable.
2) Percentages if treated as counts can be used for the χ² test.
Select the correct answer. Which statement is true about the y-intercept of a quadratic function? A. A quadratic function can only have one y-intercept. B. A quadratic function can have up to two y-intercepts. C. The y-intercept is also called a zero of the function. D. The y-intercept is located at the point where the value of y is 0.
Answer:
A. A quadratic function can only have one y-intercept.
Step-by-step explanation:
hope this helps. p.s. i really need brainliest :)
Answer:
A
Step-by-step explanation:
True or False?
The domain and range of a cube root function are always all real numbers.
Answer:
True
For the cube root function f(x)=3√x f ( x ) = x 3 , the domain and range include all real numbers. Note that there is no problem taking a cube root, or any odd-integer root, of a negative number, and the resulting output is negative (it is an odd function).
Hope that helps!
Step-by-step explanation:
What is the measure of angle x? х 59: a. 120 b. II c. 121
Answer:
option (C) 121° is right answer
Work out the equation of the line that
is parallel to the line y= 5x - 3
passes through (-2, -4)
Answer:
y = 5x +6
Step-by-step explanation:
the slope of the given equation is 5. a slope of a line parallel has the same slope. so 5
y- -4 = 5(x - -2)
y+4 = 5x +10
y = 5x +6
Suppose the population is all VCU students who track their steps each day. Among these students suppose the mean number of steps per day is 8989 with a standard deviation of 688. There are a few students who take many steps per day, and hence the distribution is skewed heavily to the right. If a simple random sample of 169 VCU students who track their steps each day is selected and the number of steps per day is determined for each, describe completely the sampling distribution of , the resulting mean number of steps per day for this sample of 169 VCU students who track their steps each day.
Answer:
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 8989 and standard deviation 52.92.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean number of steps per day is 8989 with a standard deviation of 688.
This means that [tex]\mu = 8989, \sigma = 688[/tex]
Describe completely the sampling distribution of the resulting mean number of steps per day for this sample of 169 VCU students who track their steps each day.
Sample of 169 means that [tex]n = 169[/tex]
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean [tex]\mu = 8989[/tex] and standard deviation [tex]s = \frac{688}{\sqrt{169}} = 52.92[/tex].
PLZ HELP PLZ HELP PLZ HELP WILL GIVE BRAINLY
Answer:
Steps 4 and 5
Step-by-step explanation:
Paula divided both sides in 4 and 5 to keep the equations equal.
Hope that this helps!
Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r= 4 cm
[? ]%
Round to the nearest tenth of a percent.
please help
Answer: 31.8
Step-by-step explanation:
The probability that a randomly selected point within the circle falls
in the red shaded area is; 15.9%
What is the probability?The area of the circle is gotten from the formula;
A = πr²
A = π * 4²
A = 50.265 cm²
Area of triangle = ¹/₂ * bh
Here b = h = 4. Thus;
A = ¹/₂ * 4 * 4
A = 8 cm²
Thus;
P(randomly selected is shaded) = 8/50.265
P(randomly selected is shaded) = 0.159 = 15.9%
Read more about probability at; https://brainly.com/question/25870256
Divide. Round to the nearest tenth. .48÷9.23
[tex].48 \div 9.23[/tex]
8b + 4 - 4b + 2 = what
8b+4-4b+2= 4b+6
collect the like terms and add
Please help I’ll mark you as brainliest if correct!
Answer:
♥♥♥
I tried solving this answer and got 25.2. So, I think you're answer will be 25.
Step-by-step explanation:
I divided 63 by 2.5. Hope I helped.
Choose 3 values for x that would make this inequality true.
X - 4<20
Answer:
X= 23, 22, 21, 20, 19, 18, 17 and so forth
Step-by-step explanation:
To make this inequality true then "X-4" would have to be less than 20, not equal or more than. 24-4=20 meaning the basis for the answer of X would start at 23
Which of the following would NOT be a probability?
0.23
7
15/45
2/3
Answer:
7
Step-by-step explanation:
7 is a whole number and not a probability
1 Femando exercised for twenty-five and
six-tenths minutes on Thursday. He exercised for
thirty and five-hundredths minutes on Friday. He
exercised eighteen and four-tenths minutes on
Saturday. How many total minutes did Fernando
exercise those three days?
A 74.5 C 73.85
B 73.15 D 74.05
two parallel lines are cut by a transversal what is the measure of 2
Answer:
b 80
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
A P EE X
Can someone help me?
9514 1404 393
Answer:
see below
Step-by-step explanation:
This is all about number sense: ordering and naming numbers. If you know your multiplication tables and a few key vocabulary words, that's all you need.
1a. perfect square
1b. irrational number
1c. greater than
__
2a. less than; greater than
2b. perfect square
2c. approximation
__
3a. square root
3b. square root
3c. approximation
3d. order; less than; less than
_____
When you fill in the blanks, the statements pretty much explain themselves.
__
Additional comment
For positive numbers, square and square root are operations that preserve order. That is, the square of a larger number is larger than the square of a smaller number. Likewise, the square root of a larger number is larger than the square root of a smaller number. Here, ...
81 > 64 > 44 ⇔ √81 > √64 > √44.
If a number is not a perfect square (a number multiplied by itself), then its square root is irrational.
please help.... 50% of my grade
Answer:
Ernesto's construction is wrong.
Step-by-step explanation:
Ernesto's construction is wrong.
This is because when bisecting an angle, the first thing we do is to place the compass at the vertex of the angle we want to bisect and draw an arc that will cross both lines that form the angle.
In Ernesto's case the arc drawn was not a single one but drawn separately as is seen in the image.
The arc on line AV does not continue to line VI but instead he drew another arc with different compass width on line VI before bisecting the angle.
Plz help me well mark brainliest if correct!!
Answer:
(1, 1)
Step-by-step explanation:
not 100% sure though, but hope it helps
1. Which classifications describe this figure?
2. Which classifications appear to describe both of these figures?
→ Parallelogram
→ Trapezoid
→ Quadrilateral
→ Square
→ Rhombus
→ Rectangle
Answer:
parallelogram
hope this helps you ☺️☺️
Jane ran 72 miles in 6 days. Then she tripled her rate. How long would it take her to travel 648 miles at the new speed?
Plz help.
Answer:
18 days
Step-by-step explanation:
72/6=12 miles per day
12*3=36
648/36=18 days
This graph shows a linear relationship
between the water level in a tank and time
elapsed.
Enter the initial water level, in feet, of the
water tank.
April and Cody invest $5,000 each at their local bank. April invests at a 4% simple interest rate for three years. Cody invests at a 4% compound interest rate, and earns $624.32 in interest. What is the difference in their account balances at the end of 3 years?
Answer:
106.43
Step-by-step explanation:
The difference in their account balances at the end of 3 years is $24.32
Calculations and ParametersTo solve the compound interest for Cody
First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 5,000.00(1 + 0.04/1)(1)(3)
A = 5,000.00(1 + 0.04)(3)
A = $5,624.32
To solve for the simple interest for April
P * T * R/100
5000 * 4 * 3/100
= 60,000/100
= 600.
We add the S. I of April's investment
= 5,000 + 600
= $5600.
Therefore, the difference between their account balances is $5,624.32 - $5600 = $24.32
Read more about compound interest here:
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