Answer:
The vertex is (-1, 4), the domain is all real numbers, and the range is y less than 4
Step-by-step explanation:
Given
[tex]f(x) = -(x+1)^2 + 4[/tex]
Solving (a): The vertex;
Assume the general form of a function is
[tex]f(x) = a(x-h)^2+k[/tex]
The vertex is determined by [tex](h,k)[/tex]
By comparison, we have:
[tex]-h = 1[/tex]
Solve for h, we have:
[tex]h = -1[/tex]
[tex]k = 4[/tex]
So, the vertex is:
[tex](h,k) = (-1,4)[/tex]
The domain; x is all real numbers
From the function;
[tex]f(x) = -(x+1)^2 + 4[/tex]
This can be rewritten as:
[tex]f(x) = 4 - (x+1)^2[/tex]
This implies that:
Whatever the value of [tex](x + 1)^2[/tex] is, it will be subtracted from 4 to give y or f(x);
Hence:
y is less than 4
Option B answers the question
PLEASEEEEEE HELPPPP!!!!
3)9.375 and 12 is )37.5
Solve the proportion.
Thursday
Friday
Classes
6
Hours
8
4
Hellppppp it’s a testttt!
Ratio of number of classes and the time taken to conduct each one of them on Thursday = 6 : 8
Ratio of number of classes and the time taken to conduct each one of them on Friday = c : 4
Which means :-
6 : 8 :: c : 4
6/8 = c/4
= 6 × 4 = c × 8
= 24 = 3 × 8
c = 3
The ratio = 6 : 8 :: 3 : 4
Which means that C = 3 .
Se deseneaza o dereapta si pe ea trei puncte A,B si C astfel incat C se afla intre A si B. Atunci numarul unghiurilor improprii distincte determinate de cele trei puncte este egal cu ? CAT MAI RAPID VA ROG!
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 3 − 2x, (0, 1) The equation ex = 3 − 2x is equivalent to the equation f(x) = ex − 3 + 2x = 0. f(x) is continuous on the interval [0, 1], f(0) = _____, and f(1) = _____. Since f(0) < 0 < f(1) , there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation ex = 3 − 2x, in the interval (0, 1)
Answer:
f(x) is continuous on the interval [0, 1], f(0) = -2 , and f(1) = 1.718 . Since f(0) < 0 < f(1) , there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation ex = 3 − 2x, in the interval (0, 1)
Step-by-step explanation:
From the question we are told that
The equation is [tex]f(x) = e^x - 3-2x [/tex]
The interval is [0, 1]
Generally f(0) is
[tex]f(0) = e^0 - 3-2(0) [/tex]
=> [tex]f(0) = 1 - 3-2(0) [/tex]
=> [tex]f(0) = -2[/tex]
Generally f(1) is
[tex]f(1) = e^1 - 3-2(1) [/tex]
[tex]f(1) = e^1 - 1 [/tex]
[tex]f(1) = 1.718 [/tex]
From the value we see that at x = 0 , f(0) = -2 which is below the x-axis
and the at x = 1 , f(1) = 1.718 which is above the x-axis
Now the according to Intermediate Value Theorem , given the condition stated above, there will exist a root c in the interval such that
f(c) = 0
The constant of proportionality of this table is
Cups of
blue paint
cups of
yellow paint
2 10
1
Answer:
Step-by-step explanation:
1/2
A club has 30 members is formed from 12 democrats and 18 republicans. How many different committees consisting of 8 democrats
and 8 republicans are possible to be formed?
Given:
Total number of members = 30
Number of democrats = 12
Number of republicans = 18
To find:
Number of different committees consisting of 8 democrats and 8 republicans are possible to be formed.
Solution:
Total number of ways to selecting 8 democrats from 12 democrats is
[tex]^{12}C_8=\dfrac{12!}{8!(12-8)!}[/tex]
[tex]^{12}C_8=\dfrac{12\times 11\times 10\times 9\times 8!}{8!4!}[/tex]
[tex]^{12}C_8=\dfrac{12\times 11\times 10\times 9}{4\times 3\times 2\times 1}[/tex]
[tex]^{12}C_8=495[/tex]
Total number of ways to selecting 8 republicans from 18 republicans is
[tex]^{18}C_8=\dfrac{18!}{8!(18-8)!}[/tex]
[tex]^{18}C_8=\dfrac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10!}{8!10!}[/tex]
[tex]^{18}C_8=\dfrac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}[/tex]
[tex]^{18}C_8=43758[/tex]
Now, number of different committees consisting of 8 democrats and 8 republicans are possible to be formed is
[tex]^{12}C_8\times ^{18}C_8=495\times 43758[/tex]
[tex]^{12}C_8\times ^{18}C_8=21660210[/tex]
Therefore, the total possible ways are 21660210.
3/4x-4=5/6
Rewrite so it doesn’t have any fraction
CHECK PHOTO Intercepts of the graph BE SURE TO BE CORRECT PLEASE no work needed
Answer:
y= (0, .7)
x= (-1.2, 0)
Step-by-step explanation:
r u taking a test?
The ratio of chocolate
chip cookies to total
cookies on a tray is 3:5.
What percent of the tray
is chocolate chip
cookies?
Answer:
The percent is 75%
Step-by-step explanation:
A sphere has a diameter of 8cm. Which statements about the sphere are true? Check all that apply.
• the sphere has a radius of 4cm.
• the sphere has a radius of 16 cm.
• The diameter’s length is twice the length of the radius.
• The radius’s length is twice the length of the diameter.
• The volume of the sphere 2048/3 pi. cm. cubed
• the volume of the sphere is 256/3 pi. cm. cubed
Answer:
The sphere has a radius of 4 cm.The diameter’s length is twice the length of the radius.The volume of the sphere is StartFraction 256 Over 3 EndFraction pi centimeters cubed.Step-by-step explanation:
Answer:
1. The sphere has a radius of 4 cm.
3. The diameter length is twice the length of the radius.
6. The volume of the sphere is StartFraction 256 Over 3 EndFraction pi centimeters cubed.
Convert the measurement:
3 inches to centimeters
O 7.00 cm
0 2.78 cm
O 8.21 cm
O 7.62 cm
Step-by-step explanation:
ans is 7.62
1 inch =2.54cm
2.54 multiplied by 3=7.62
What is the slope of the line represented by the equation 2x + 3y= -12. (A)- 3/2. (B)-2/3. (C) 2/3. (D) 3/2
Answer:
-2/3
Step-by-step explanation:
Here, we need to rearrange the equation into slope intercept form:
[tex]2x + 3y = -12[/tex]
subtract 2x on both sides:
[tex]3y = -2x-12[/tex]
divide 3 on both sides:
[tex]y = \frac{-2}{3} x + 4[/tex]
Finally, we get it in the form y = mx + b. We know that in that form, m is the slope so that means, the slope is -2/3
A die is rolled thrice. What is the probability that the sum of
the rolls
rolls is atleast 5
Answer:
1 out of 6
Step-by-step explanation:
no matter how many times you roll it the chances will always be the same
Answer:
there is a 1/6 chance
Step-by-step explanation:
there are 216 total combinations but only 36 combinations that end in 5.
36/216 = 1/6.
Hope this helps!
An automatic teller machine gives you $150 in five and ten-dollar bills. There are two more than twice as many five-dollar bills as there are ten-dollar bills. How many of each denomination are there?
Answer:
There are 7 ten-dollar bills and 16 five-dollar bills.
Step-by-step explanation:
Let's call:
T: Number of ten-dollar bills
F: Number of five-dollar bills
The amount of money withdrawn from the ATM is $150:
10T+5F=150
Dividing by 5:
[tex]2T+F=30\qquad\qquad [1][/tex]
We also know there are two more than twice as many five-dollar bills as there are ten-dollar bills:
[tex]F=2+2T\qquad\qquad [2][/tex]
Substituting [2] into [1]:
2T+2T+2=30
Rearranging:
2T+2T=30-2
Simplifying:
4T=28
Solving:
T=28/4=7
From [2]:
F=2+2*7=2+14=16
There are 7 ten-dollar bills and 16 five-dollar bills.
Mai says that -8 > -4 . Do you agree with her? Explain or show your reasoning.
Answer:
No
Step-by-step explanation:
-8 is less than -4. Negative numbers reverse the logic of positive ones: since positive 8 is more than positive 4, negative 8 is less than negative 4.
Jernardia is running a 5-kilometer race at a constant pace. After running for 20 minutes, she completes 4 kilometers. After running for 30 minutes, she
completes 5 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers,
represent the dependent variable.
Which equation can be used to represent k, the number of kilometers Jerardia runs in t minutes?
Oy-5= 1(x - 30)
O y-30 = 10 (x - 5)
Oy-30 = -10 (x - 5)
Oy-30 = 0.1 (x - 5)
Answer:
oy-5=1 ( x-30)
Step-by-step explanation:
jernardia is dumb as heck
I need help asap! Ill make you brainiest if answer
Answer:
43
Step-by-step explanation:
5 × 3 - 7 × -4 =
15 - - 28 =
15 + 28 = 43
Answer:
43
Step-by-step explanation:
5a - 7b if a = 3 and b = -4
= 5(3) - 7(-4)
= 15 - -28
= 15+28
= 43
A vaccine is 95 percent effective. What is the probability that it is not effective for more than 1 out of 20 individuals?
Answer:
The probability that the vaccine is not effective in more than 1 of the 20 individuals is equal to:
P = 1 - P(1) - P(0)
Where:
P(1) = probability that the vaccine is not effective in one individual
P(0) = probability that the vaccine is not effective in 0 individuals.
The probability that the vaccine is effective is 0.95
Then the probability that the vaccine is not effective is 0.05.
Then to calculate P(1), suppose that the vaccine is not effective in the first case and then is effective 19 times, this is:
p(1) = (0.05^1)*(0.95^19)
But this only for one case, we have 20 possible permutations (the vaccine is not effective in the first case, the second case, third case, etc)
Then the actual probability is:
P(1) = 20*((0.05^1)*(0.95^19)) = 0.377
And P(0) is easy to compute:
P(0) = (0.05^0)*(0.95^20) = 0.358
And here we have only one possible permutation, so we do not worry about that.
Then P = 1 - P(1) - P(0) = 1 - 0.377 - 0.358 = 0.265
This means that the probability that the vaccine is not effective in more than one individual is of 0.265 (or 26.5% in percentage form)
10) A triangle is shown above. Glo Metri claims that the Pythagorean Theorem
can be used to solve for the missing side length x. Is Gio's claim correct? Why or
why not?
A. No, Gio's claim is incorrect because the Pythagorean theorem can only be used
when the side lengths of a triangle are square numbers.
B. No, Gio's claim is incorrect because the Pythagorean theorem can only be used
with a right triangle.
C. Yes, Gio's claim is correct because the Pythagorean theorem can be used to find
the missing side in any triangle.
D. Yes, Gio's claim is correct because the Pythagorean theorem can be used with any
triangle that is approximately right.
Answer:
B. No, Gio's claim is incorrect because the Pythagorean theorem can only be used
with a right triangle.
Step-by-step explanation:
The pythagorean theorem which is given as a² + b² = c², only applies to right triangles. Where, c is the hypotenuse side length that is opposite to the right angle of the triangle, while a and b are the two other legs of the right triangle.
The triangle given above is not a right angle. The measure of the missing length = 180 - (60 + 40) = 80°.
A right ∆ has an angle measure of 90°. Therefore, the pythagorean theorem cannot be applied in this case to solve for the missing side length, x.
So, Gio's claim is INCORRECT.
Piper and her children went into a movie theater and she bought $59.50
bags of popcorn and candies. Each bag of popcorn costs $8.50 and each candy costs
$4.25. She bought 8 more candies than bags of popcorn. Graphically solve a system
of equations in order to determine the number of bags of popcorn, x, and the number
of candies, y, that Piper bought.
6 candy boxes
Step-by-step explanation :
Since they both bought their own popcorn that means they both spent $8 on popcorn making that a total of $16. Therefore we now only need to find one variable which is the number of candy boxes that they bought in order to reach the $25 total that they spent. This variable can be represented as x in the following algebraic equation.
(2*8) + 1.50x = 25
16 + 1.50x = 25 ... subtract 16 from both sides
1.50x = 9 ... divide both sides by 1.50
x = 6
Finally, we can see that Billy and Tommy bought a total of 6 candy boxes.
Answer:
This is the answer on Delta Math
Step-by-step explanation:
Does this set of ordered pairs represent a function? Why or why not? -1,5), (0, -3), (2, 7), (4,0), (7, 5)) A. No, because two of the y-values are the same. OB. Yes, because there are two xvalues that are the same. OC. Yes, because every xvalue corresponds to exactly one yvalue D. No, because one xvalue corresponds to two different values.
Answer:
C.
Step-by-step explanation:
All the x-values are different and go to one y-value.
Yes this set of ordered pairs represent a function because every x value corresponds to exactly one y value
What are ordered pairs in sets?A function f from a set A to a set B is a set of ordered pairs {(x, y)} such that x in the set A and y is the in the B. For every x ∈ A there is exactly one y ∈ B such that (x, y) is an ordered pair in f. We call this element f(x). We call A the domain and we call B the range.
How do you determine if a set of ordered pairs are functions?A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate. An equation that produces such a set of ordered pairs defines a function.
According to the question
Set of ordered pairs represent a function :
(-1,5), (0, -3), (2, 7), (4,0), (7, 5)
As we can observe that every point have different x value for there respective y ,
and A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate.
Hence, Yes, this set of ordered pairs represent a function because every x value corresponds to exactly one y value
To know more about ordered pairs in sets here:
https://brainly.com/question/12941484
#SPJ2
In multiple regression analysis, the word linear in the term "general linear model" refers to the fact that β0, β1, . . ., βp all have exponents of a. at least 1. b. less than 0. c. 0. d. 1.
Answer:
d. 1
Step-by-step explanation:
it is called linear because β0, β1, . . ., βp all have their exponents to be 1. A multiple linear regression is a type of regression which has more than one independent variable. it tells us the existing relationship between 2 or more of these independent variables on the dependent variable. for it to be regarded to be linear, it is very important that the exponents be equal to 1. else it could be quadratic.
what is the slope of this line -1/3, -2/3,2/3,1/3
Answer:
(-5,9),(3,0)
(0,1),(1,0)
(1,2),(3,4)
Step-by-step explanation:
I hope this helps!
Answer: It's 2/3
Step-by-step explanation:
What is the other solution to the equation?
A: x=-6
B: x=-4
C: x=2
D: x=4
Answer:
to what
Step-by-step explanation:
i can't see the question
Which expression is a prime polynomial
What are the expressions?
I need help ASAP please
A normal population has mean =μ7 and standard deviation =σ5. (a) What proportion of the population is less than 18?
Answer:
P(x< 18) = 0.986
Step-by-step explanation:
Step 1: find the z-score using the formula, z = (x - µ)/σ
Where,
x = randomly chosen values = 18
µ = mean = 7
σ = standard deviation = 5
Proportion of the population that is less than 18 = P(x < 18)
Plug in the values into z = (x - µ)/σ, to get z-score.
z = (18 - 7)/5
z = 11/5 = 2.2
Step 2: Find P(x< 18) = P (z<2.2) using z-table.
The probability that corresponds with z-score calculated is 0.986.
Therefore,
P(x< 18) = 0.986
HELPPPPP!! Is the expression 6 + 3 = 9 an equation ? Explain.
Answer:
No, because an expression is already solved and an equation is where you have to solve it
Step-by-step explanation:
Answer:
No as said you have to solve and equation yet an expression is already solved for your viewing.
Step-by-step explanation:
Choose the equation that represents the line passing through the point -3 and -1 with a slope of 4
Answer:
y=4x+11
Step-by-step explanation:
y=mx+b.
-1=4(-3)+b
-1= -12+b
+12 +12
11=b
Answer:
y = 4x + 11
Step-by-step explanation:
How do you do these 2 questions?
Answer:
0 ≤ an ≤ bn
The series ∑₁°° bn converges
The series ∑₁°° an converges by comparison to ∑₁°° bn.
0 ≤ an ≤ bn
The series ∑₁°° bn diverges
The comparison test is inconclusive for our choice of bn.
Step-by-step explanation:
an = 1 / (n² + n + 3) and bn = 1 / n²
The numerators are the same, and the denominator of an is greater than the denominator of bn. So 0 ≤ an ≤ bn.
bn is a p series with p > 1, so it converges.
Since the larger function converges, the smaller function also converges.
an = (3n − 1) / (6n² + 2n + 1) and bn = 1 / (2n)
If we rewrite bn as bn = (3n − 1) / (6n² − 2n), we can tell that when the numerators are equal, the denominator of an is greater than the denominator of bn. So 0 ≤ an ≤ bn.
bn is a p series with p = 1, so it diverges.
The larger function diverges. We cannot conclude whether the smaller function converges or diverges.