Answer:
-5
Step-by-step explanation:
If the second equation is multiplied by 4, the coefficient of the x-variable will be 5·4 = 20. To eliminate the x-variable by addition, the first equation needs to be multiplied by a value that will result in an x-coefficient of -20. If that value is k, then we have ...
4k = -20
k = -20/4 = -5
The first equation should be multiplied by -5 to eliminate the x-variable by addition.
_____
Comment on general case
In general, if you have ...
ax +by = c
dx +ey = f
to eliminate the x-variable by addition, you can multiply the second equation by "a" and the first equation by "-d". In the problem above, those numbers are 4 and -5.
Answer:
-5
Step-by-step explanation:
A celebrity called Wayne East has been having some money problems recently. He is thinking of investing in the greatest record in the world, and wants to know how the value will change over time. He has an exponential regression model where his predictor is time in months, and response variable is money, measured in thousands of dollars. The alpha value is 4.2, and beta is 1.03. Based on this model, how much money (in thousands) will he have after six months
Answer:
Wayne west would have $5,015 in six months
Step-by-step explanation:
The formula for exponential regression model is y = αβˣ
Where y is amount of money in 1000 dollars
x is time in months
We are given that α = 4.2 and β = 1.03 and x = 6 months
Therefore, based on this model, y = αβˣ, the amount he would have in 6 months, y = [tex]4.2*(1.03) ^{6}[/tex]
y = 5.015 × 1000 = $ 5,015
What is the measure of angle A?
Answer:
A = 19.47
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin A = 2/6
Take the inverse sin of each side
sin ^-1 ( sin A) = sin ^-1 (2/6)
A =19.47122063
To the nearest hundredth
A = 19.47
Please help ASAP! I will mark BRAINLIEST! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answer:
D. 96
F. 32
Step-by-step explanation:
The inequality 3x ≥ 96, means that x and 3 must be multiplied to get a product that is greater than 96. So to figure this out, you must plug in the numbers given for x, like so:
3x ≥ 96
A. 3(31) ≥ 96
93 ≥ 96 This is incorrect since 93 is not greater than 96
A tip that makes this easier is that, you can see that 31 multiplied by 3 is 93, which is only a couple numbers off 96, so all numbers after 31 will result in a product greater than 96. For example:
D. 3(96) ≥ 96
288 ≥ 96 This inequality is correct
F. 3(32) ≥ 96
96 ≥ 96
The inequality sign states that the number must be either greater or equal to 96, which it is.
what is the cube root of 1
Answer:
1.
Step-by-step explanation:
∛1= 1.
It can also be seen as:
1×1×1= 1.
6
An ordinary fair dice is thrown once.
(a) On the probability scale mark with a cross (X) the probability ti
the dice lands on an even number.
1
2
(b) Write down the probability that the dice lands on a number les
than 3.
Answer:
(a) 1/2(b) 1/3Step-by-step explanation:
(a) 3 of the 6 numbers on the die are even, so the probability that one of them will show is 3/6 = 1/2.
__
(b) 2 of the 6 numbers on the die are less than 3, so the probability that one of them will show is 2/6 = 1/3.
What is the number of possible permutations of 5 objects taken 2 at a time? A. 10 B. 20 C. 60 D. 120
Answer:
B. 20
Step-by-step explanation:
5P2 is equal to 20 using the permutation formula.
To the nearest tenth of a cubic centimeter, what is the volume of
the sphere if r = 17 cm?
Answer:
V≈20579.53
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3[/tex]
will mark the branliest to first one who answers
Answer:
3 1/4
Step-by-step explanation:
3/4 + (1/3 ÷1/6) - (-1/2)
Subtracting a negative is adding
3/4 + (1/3 ÷1/6) +1/2
Parentheses first
Copy dot flip
3/4 + (1/3 * 6/1) +1/2
3/4 + 2 + 1/2
Get a common denominator
3/4 + 2 + 2/4
2 + 5/4
2 + 4/4 +1/4
2+1 + 1/4
3 1/4
Suppose you had to
guess on a four-choice
multiple-choice test and
were given four questions.
Find the binomial
probability distribution.
( + ) ℎ =
4 = 0.25
Answer:
For 0 correct answer [tex]^4c_0p^0q^{4-0}[/tex]
For 1 correct answer [tex]^4c_1p^1q^{4-1}[/tex]
For 2 correct answer [tex]^4c_2p^0q^{4-2}[/tex]
For 3 correct answer [tex]^4c_3p^1q^{4-3}[/tex]
For 4 correct answer [tex]^4c_4p^1q^{4-4}[/tex]
Step-by-step explanation:
It is given that there are 4 questions n = 4
Number of choices is 4
So probability of getting correct answer [tex]=\frac{1}{4}[/tex]
Probability of getting incorrect answer [tex]=1-\frac{1}{4}=\frac{3}{4}[/tex]
Probability distribution is given by [tex]^nc_rp^rq^{n-r}[/tex]
Therefore probability distribution of 0 correct answer
[tex]^4c_0p^0q^{4-0}[/tex]
Therefore probability distribution of 1 correct answer
[tex]^4c_1p^1q^{4-1}[/tex]
Therefore probability distribution of 2 correct answer
[tex]^4c_2p^0q^{4-2}[/tex]
Therefore probability distribution of 3 correct answer.
[tex]^4c_3p^1q^{4-3}[/tex]
Therefore probability distribution of 4 correct answer.
[tex]^4c_4p^1q^{4-4}[/tex]
Junior bought a bag of mixed fruit snacks. The flavors in the bag are 4 strawberry, 3 cherry, and 5 grape. If he chooses one fruit snack at random, what it the probability of the first one being grape?
Answer:I believe it would be 5/12
Step-by-step explanation:
You add all of them up then since it's 5 grapes and in total there is 12 fruit snacks. It should be 5 grapes of 12 fruit snacks in the bag.
Equations
What is the solution of the system of linear equations?
-3x + 4y = -18
2x - y = 7
(-2,-3)
(-2,3)
(2, -3)
(2, 3)
Answer:
Step-by-step explanation:
-3x + 4y = -18
8x - 4y = 28
5x = 10
x = 2
4 - y = 7
-y = 3
y = -3
(2, -3)
The solution of the system of linear equations given is (2,-3), the correct option is C.
What is System of Linear Equation?The system of linear equation is set of equations which have a common solution.
The equations are
-3x+4y = -18
2x-y =7
The linear equations can be solved using substitution method
y = 2x -7 from equation 2 will be substituted in equation 1
-3x +4 ( 2x -7) = -18
-3x +8x -28 = -18
5x = 10
x = 2
y = 2 * 2 -7 = -3
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A footbridge has a span of 54 feet. A sign is
to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge?
Answer:
27
Step-by-step explanation:
Because if it is halfway, that means
halfway=1/2
1/2=1/2 of 54
54/2 or 1/2 of 54=27
PLS MARK ME BRAINLIEST I NEED IT PLEASE
The center of the sign will be 27 feet apart from both ends of the bridge.
Given that,
A footbridge has a span of 54 feet. A sign is to be placed exactly halfway across the bridge. How far will the center of the sign be from each end of the bridge is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Since the bridge is 54 feet long,
Now at the center of the bridge, a sign is placed,
So the distance of sign from both ends is equal to half of the total length of the bridge. i.e.
= 54 / 2
= 27
Thus, the center of the sign will be 27 feet apart from both ends of the bridge.
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Which expression is equivalent to m n + z?
n m + n
z + m z
m z + n
z + n m
Answer:
z + n m
Step-by-step explanation:
These expressions are equivalent because the commutative property of addition, which states that when adding two terms, the order doesn't matter.
If this answer is correct, please make me Brainliest!
Answer:
It's "c"
Step-by-step explanation:
i just did this on edge
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answer:
19.5 in²
Step-by-step explanation:
Area of rhombus tile = side × height
Area = 3 × 6.5
Area = 19.5 in²
A rhombus, like any parallelogram, has area equal to base times height,
that's 3×6.5 = 19.5 square inches
Answer: 19.5
Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of 40.1 and standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude?
Answer:
[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]
The degrees of freedom are
[tex]df=20+20-2=38[/tex]
And the p value is given by:
[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Step-by-step explanation:
When we have two independent samples from two normal distributions with equal variances we are assuming that
[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]
And the statistic is given by this formula:
[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]
Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:
[tex]S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]
The system of hypothesis on this case are:
Null hypothesis: [tex]\mu_1 = \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]
We have the following data given:
[tex]n_1 =20[/tex] represent the sample size for group 1
[tex]n_2 =20[/tex] represent the sample size for group 2
[tex]\bar X_1 =43.5[/tex] represent the sample mean for the group 1
[tex]\bar X_2 =40.1[/tex] represent the sample mean for the group 2
[tex]s_1=4.1[/tex] represent the sample standard deviation for group 1
[tex]s_2=3.2[/tex] represent the sample standard deviation for group 2
First we can begin finding the pooled variance:
[tex]\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525[/tex]
And the deviation would be just the square root of the variance:
[tex]S_p=3.678[/tex]
The statistic is givne by:
[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]
The degrees of freedom are
[tex]df=20+20-2=38[/tex]
And the p value is given by:
[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Using the t-distribution, as we have the standard deviation for the sample, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.
What are the hypothesis tested?At the null hypothesis, it is tested if there is no difference, that is:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, it is tested if there is a difference, that is:
[tex]H_a: \mu_1 - \mu_2 \neq 0[/tex]
What is the mean and the standard error of the distribution of differences?For each sample, we have that they are given by
[tex]\mu_1 = 43.5, s_1 = \frac{4.1}{\sqrt{20}} = 0.9168[/tex]
[tex]\mu_2 = 40.2, s_2 = \frac{3.2}{\sqrt{20}} = 0.7155[/tex]
Hence, for the distribution of differences, the mean and the standard error are given by:
[tex]\overline{x} = \mu_1 - \mu_2 = 43.5 - 40.2 = 3.3[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.9168^2 + 0.7155^2} = 1.163[/tex]
What is the test statistic?It is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{3.3 - 0}{1.163}[/tex]
[tex]t = 2.84[/tex]
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 20 + 20 - 2 = 38 df, the critical value is of [tex]|z^{\ast}| = 2.0244[/tex].
Since the absolute value of the test statistic is greater than the critical value, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.
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Sara goes on a slingshot ride in an amusement park. She is strapped into a spherical ball that has a radius of centimeters. What is the volume of air in the spherical ball? Use this formula: , where r is the sphere’s radius.
A.
B.
C.
D.
Answer:
A. 4×π×3²×[tex]10^{6}[/tex]
Step-by-step explanation:
r = 3×10² = 3×100 = 300
[tex]\frac{4}{3}[/tex]×π×300³=
[tex]\frac{4}{3}[/tex]×π×27,000,000=
[tex]\frac{108,000,000}{3}[/tex]×π=
36,000,000π
Answers solved:
A. 36,000,000π
B. 108,000,000π
C. 3,600,000π
D. 32,400,000π
The solution is Option A.
The volume of the air in the spherical ball is given by the equation
V = 4π ( 3 )² ( 10 )⁶ cm³
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the volume of the sphere be represented as V
Now , the radius of the spherical ball be r
The value of r = 3 ( 10 )² cm
So , the volume of the spherical ball = ( 4/3 ) πr³
Substituting the values in the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x [ 3 ( 10 )² ]³
On simplifying the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x ( 3 )³ ( 10 )⁶
Volume of the spherical ball V = 4 x π x ( 3 )² ( 10 )⁶
Therefore , the value of V is 4π ( 3 )² ( 10 )⁶
Hence , the volume of the spherical ball is 4π ( 3 )² ( 10 )⁶
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In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foot.
Answer:
21
Step-by-step explanation:
Answer:
6.7
Step-by-step explanation:
Drag each tile to the correct box. Not all tiles will be used.
Arrange the equations in the correct sequence to find the inverse of f(x) = y = 3x / 8 + x
Answer:
Inverse of f(x)
[tex]f^{l} (x) = \frac{8 x}{3-x}[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given the function
[tex]f(x) = \frac{3 x}{8+x}[/tex]
Given function is one-one and onto function
Hence f(x) is bijection function
[tex]y = f(x) = \frac{3 x}{8+x}[/tex]
now cross multiplication, we get
( 8+x)y = 3 x
8 y + x y = 3 x
8 y = 3 x - x y
taking Common 'x' we get
x (3 - y) = 8 y
[tex]x = \frac{8 y}{3-y}[/tex]
Step(ii):-
The inverse function
[tex]x = \frac{8 y}{3-y} = f^{l}(y)[/tex]
The inverse function of x
[tex]f^{l}(x) = \frac{8 x}{3-x}[/tex]
Final answer:-
Inverse of f(x)
[tex]f^{l} (x) = \frac{8 x}{3-x}[/tex]
Solve 20x = 10 for x. A. x = 1/2 B. x = 1.5 C. x = 2 D. x = 10
Answer:
A. 1/2
Step-by-step explanation:
20x=10
Divide 20 on both sides of the equation to get x by itself
20x=10
___. __
20. 20
x =1/2
Answer:
A) x= 1/2
Step-by-step explanation:
20x= 10 we then divide 10 by 20 to get x= 10/20 or if we simplify x= 1/2. Thus answer choice A) is correct!
how many tenths are in 4600
Answer:
4600 tenths as a Fraction
Since 4600 tenths is 4600 over ten, 4600 tenths as a Fraction is 4600/10.
4600 tenths as a Decimal
If you divide 4600 by ten you get 4600 tenths as a decimal which is 460.00.
4600 tenths as a Percent
To get 4600 tenths as a Percent, you multiply the decimal with 100 to get the answer of 46000 percent.
4600 tenths of a dollar
First we divide a dollar into ten parts where each part is 10 cents. Then we multiply 10 cents with 4600 and get 46000 cents or 460 dollars and 0 cents.
Step-by-step explanation:
Hope this helped!
Stay safe!!!
Answer:
Step-by-step explanation:
To answer this, multiply 4600 by 10: 46000. There are 46000 tenths in 4600.
Two terms of an arithmetic sequence are a12=70 and a30=124. Write an explicit rule for the nth term.
Answer:
Tn = 34-3nStep-by-step explanation:
The formula for calculating the nth term of an arithmetic sequence is given as;
Tn = [tex]a+(n-1)d[/tex]
a is the first term
n is the number of terms
d is the common difference
If two terms of an arithmetic sequence are a12=70 and a30=124 then;
T12 = a+(12-1)d = 70
T12 = a+11d = 70...(1)
T30 = a+(30-1)d = 124
T30 = a+29d = 124...(2)
Solving equation 1 and 2 simultaneously to get a and d;
Taking the difference of both equation we have;
29d - 11d = 124-70
18d = 54
d = 54/18
d = 3
Substituting d=3 into equation 1 to get the value of 'a' we have;
a+11(3) = 70
a+33=70
a = 70-33
a = 37
To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3
Tn = 37+(n-1)3
Tn = 37+3n-3
Tn = 34-3n
This gives the required nth term
What is the area of the triangle
Answer:
A. 6 inchesssssssss
Answer:
6
Step-by-step explanation:
Simplify the expression below.
14a8y3 - 7 Ay5 + 28a12y2
7aty
A.
OB.
2a²y3 - ay5 + 4a3y2
2a4y? - JA + 428 y
2a4y3 – 5 + 428 y?
D. 2012,4 - 2876 +4215,3
C.
Answer:
14a8y3 - 7 Ay5 + 28a12y2- 7ay2 • (4a11 + 2a7y - y3)
Step-by-step explanation:
Equation at the end of step 1 :
(((14•(a8))•(y3))-(7a•(y5)))+((22•7a12)•y2)
Step 2 :
Equation at the end of step 2 :
(((14•(a8))•(y3))-7ay5)+(22•7a12y2)
Step 3 :
Equation at the end of step 3 :
(((2•7a8) • y3) - 7ay5) + (22•7a12y2)
Pull out like factors
Answer: 7ay2 • (4a11 + 2a7y - y3)
Hope this helps.
Im a parent for a 5th grader and don't remember this, plz help?
Again,
Josh wants to make 5 airplane propellers. he needs 18 centimeters of wood for each propeller. how many centimeters of wood will he use? How can I help him understand this problem.
Answer:
90 cm.
Step-by-step explanation:
One airplane propeller needs 18 centimetres of wood.
Josh wants to make 5 of them.
So, we would have to take the '18' centimetres of wood and multiply by 5 to get the total for all 5 pieces.
[tex]\text{Number of Propellers} * 18 \text{ Centimetres}[/tex]
[tex]5 * 18 = 90[/tex]
Josh should need 90 centimetres of wood total to make 5 airplane propellers.
Please help ASAP! Will give BRAINLIEST! Please read the questionTHEN answer correctly! No guessing.
Answer:D
Step-by-step explanation:
(4/5)^0
4^0/5^0=1/1=1
Sam conducted a survey to determine your favorite flavor of ice cream is his hometown. 15 of the 50 people he surveyed liked strawberry best. How many of the 3,500 residents in the town would you expect to like strawberry best
Answer: 1050 people.
Step-by-step explanation: It's a rule of three question.
15/50 as x/3500
Then you have that 50x = 52500
x = 1050
There you have it.
A music professor offers his 40 students the option of coming to an additional rehearsal session the week before their juries (musical final exams.) In order to decide whether these extra sessions actually help students, he keeps track of who attends them and compares their jury scores to those of students who did not schedule extra sessions. This study is a(n): A) matched pairs design. B) randomized block design. C) nonrandomized experiment. D) observational study. E) completely randomized experiment.
Answer:
D. Observational Study
Explanation:
An observational study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.
This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study is subject to bias because a positive or negative result might be because of other factors not related to the study.
5×60=5×___tens
=_____tens
=______
Answer:
300
Step-by-step explanation:
5x60=5x6 tens it equal to 30 tens. 30 tens equals 300
Answer:
see below
Step-by-step explanation:
there are 6 tens in 60!
5x60 = 5 x 6 tens
= 30 tens
= 300
Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C? On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3). A Is congruent to B and B Is congruent to C A Is congruent to A, B Is congruent to B, C Is congruent to C Each triangle is a right triangle. Each triangle is an isosceles triangle.
Answer:
A Is congruent to B and B Is congruent to C
Step-by-step explanation:
Let's look at the answer choices:
A: "A Is congruent to B and B Is congruent to C"
Well, clearly, if A ≅ B and B ≅ C, then by the transitive property, we can say that A ≅ C. So, A is very likely correct.
B: "A Is congruent to A, B Is congruent to B, C Is congruent to C"
Just because A is congruent to itself (and same with B and C) doesn't necessarily mean that they're congruent to each other. So, B is wrong.
C: "Each triangle is a right triangle."
Again, there are so many right triangles out there with different dimensions. For example, there are some with sides 3, 4, and 5, and others with sides 5, 12, and 13. They are not congruent, however. So, rule out C.
D: "Each triangle is an isosceles triangle."
This is just like choice C since there are so many variations of isosceles triangles. So D is wrong.
The answer is thus A.
Answer:
First one:
A Is congruent to B and B Is congruent to C
Step-by-step explanation:
Since B is obtained by translating A, it has the same measure angles and sides as A, hence B is congruent to A
C is obtained by reflecting B, which doesn't alter the measure of sides and angles, so C is congruent to B
Therefore by transition, C is congruent to A
If the base-ten blocks shown are to be divided into 5 equal groups, what should be done first?
Answer:
2 divided
Step-by-step explanation:
