Answer:
[tex]10a + 5(a - 3) = 15 \\ 10a + 5a - 15 = 15 \\ 15a = 30 \\ a = \frac{30}{15} \\ a = 2 \\ 10 \times 2 + 5(2 - 3) = 15 \\ 20 + - 5 = 15 \\ 15 = 15 \\ lhs = rhs\\ thank \: you[/tex]
Answer: a = 2
Solve:
Given
10a + 5 (a - 3) = 15
Expand parentheses and apply the distributive property
10a + 5 · a - 5 · 3 = 15
10a + 5a - 15 = 15
Combine like terms
(10a + 5a) - 15 = 15
15a - 15 = 15
Add 15 on both sides
15a - 15 + 15 = 15 + 15
15a = 30
Divide 15 on both sides
15a / 15 = 30 / 15
[tex]\boxed{a=2}[/tex]
Check:
Left-hand side = 10a + 5 (a - 3)
Left-hand side = 10(2) + 5 (2 - 3)
Left-hand side = 20 + 5(-1)
Left-hand side = 20 - 5
Left-hand side = 15
Right-hand side = 15
15 = 15, therefore, [tex]\boxed{a=2}[/tex] would make the equation true.
Hope this helps!! :)
Please let me know if you have any questions
Convert 6 feet to miles ( round five decimal places
Answer:
0.00114
Step-by-step explanation:
Divide length value by 5280
A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by performing yoga exercises. A treatment group and a control group are selected. The sample statistics are given below. Construct a 90% confidence interval for the difference between the two population means, Would you recommend using yoga exercises? Treatment Group Control Group n1 = 100 n2 = 100 1 = 178 2 = 193 s1 = 35 s2 = 37
Answer:
90% confidence interval for the difference between the two population means
( -23.4166 , -6.5834)
Step-by-step explanation:
Step(i):-
Given first sample size n₁ = 100
Given mean of the first sample x₁⁻ = 178
Standard deviation of the sample S₁ = 35
Given second sample size n₂= 100
Given mean of the second sample x₂⁻ = 193
Standard deviation of the sample S₂ = 37
Step(ii):-
Standard error of two population means
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]
Degrees of freedom
ν = n₁ +n₂ -2 = 100 +100 -2 = 198
t₀.₁₀ = 1.6526
Step(iii):-
90% confidence interval for the difference between the two population means
[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]
(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)
(-15-8.4166 , -15 + 8.4166)
( -23.4166 , -6.5834)
In the diagram, ∆ABC and ∆DBE are similar. What is the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE? A. 1.33 B. 0.75 C. 0.66 D. 0.55
Answer:
B
Step-by-step explanation:
Calculate the ratio of corresponding sides, image to preimage, that is
scale factor = [tex]\frac{DE}{AC}[/tex] = [tex]\frac{12.09}{16.12}[/tex] = 0.75 → B
The scale factor of the dilation will be 1.33. Then the correct option is A.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
In the diagram, ∆ABC and ∆DBE are similar.
Then the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE will be
⇒ 16.12 / 12.09
⇒ 1.33
Then the correct option is A.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ2
Convert 4.206 m into mm
Answer:
4206 is the answer of this question
Answer:
I think it will help you a lot.
which of the following illustrates commutative property of addition? 17+4=4+17
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Answer:
17 +4 = 4 +17
Step-by-step explanation:
The only expression shown here illustrates that property.
In the adjoining figure, in ΔABC, D is the midpoint of the side BC.Hence a) AD is ___________ A b) AM is ____________ c) Is BD = DC please help!!!!!!!!!!!!!!
Answer:
a) AD is Median
b) AM is Perpendicular Bisector
Step-by-step explanation:
c) Yes because the Median divides the line into two equal parts
What is the measure of ∠x?
Angles are not necessarily drawn to scale.
∠x= ____∘
Please help me!
Answer:
hey mate ...
105 + JID = 180 ( STRAIGHT LINE )
JID = 75
NOW APPLY ANGLE SUM IN TRIANGLE JID
75 + 39 + IJD = 180
IJD = 66
x = IJD by vertically opposite angles
x = 66
Do not use spaces in your answer. Solve for x. -5x + 12x - 8x = -24 x = ___ a0
Answer:
[tex]\Huge \boxed{x=24}[/tex]
Step-by-step explanation:
[tex]-5x + 12x - 8x = -24[/tex]
Combine all like terms.
[tex](-5+ 12- 8)x = -24[/tex]
[tex]-x=-24[/tex]
Multiply both sides by -1.
[tex]x=24[/tex]
Answer:
x must be 24
Step-by-step explanation:
I assume you meant " -5x + 12x - 8x = -24
Combine the x terms on the left side, obtaining -x = -24.
Then x must be 24
A researcher surveys middle-school students on their study habits. She finds that in a random sample of 28 middle-school students, the mean amount of time that they spend working on the computer each night is 2.4 hours with a standard deviation of 0.92 hours. She uses the sample statistics to compute a 95% confidence interval for the population mean - the the mean amount of time that all middle-school students spend working on the computer each night. What is the margin of error for this confidence interval
Answer:
The margin of error is [tex]E = 1.96 * \frac{ 0.92}{\sqrt{28 } }[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 28[/tex]
The sample mean is [tex]\= x = 2.4 \ hr[/tex]
The standard deviation is [tex]\sigma = 0.92 \ hr[/tex]
Given that the confidence level is 95% the the level of significance can be evaluated as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 0.92}{\sqrt{28 } }[/tex]
[tex]E = 0.3408[/tex]
Today only, a suit is being sold at a 26% discount. The sale price is $259.
What was the price yesterday?
Answer:
$350
Step-by-step explanation:
1. Set up the equation. The sale price of $259 is 74% of the original price.
[tex]\frac{74}{100}[/tex] = [tex]\frac{259}{x}[/tex]
2. Cross multiply
74x = 25900
3. Solve
x = 350
A city council consists of seven Democrats and six Republicans. If a committee of five people is selected, find the probability of selecting two Democrats and three Republicans.
Answer:
solution,
let d and r denote democrats and republicans respectively.
given,
no. of total sample space n(s) =7+6=13
no. of total democrats n(d)=7
no. of total republicans n(r)=6
no. of democrats events n(D1)=2
no. of republicans events n(R1)=3
it is a mutually exclusive event. so the probability of selecting two democrats and three republicans= {n(D1)/n(s)} * {n(r1)/n(s)}
=(2/13)*(3/13)
=6/169
Answer:
6/169
Step-by-step explanation:
The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing quadratically? x f(x) g(x) 1 3 3 2 6 9 3 11 27 4 18 81 5 27 243 f(x), because it grows faster than g(x) g(x), because it will not intersect f(x) g(x), because it grows slower than f(x) f(x), because it grows slower than g(x)
Answer:
D
Step-by-step explanation:
Exponential functions always will end up being bigger than quadratic functions and since g(x) is probably the exponential it makes f(x) the quadratic because it is growing slower than the function g(x)
The function g(x) increases faster than the function f(x). Then the correct option is D.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The table below shows the values of f(x) and g(x) for different values of x.
One of the functions is a quadratic function, and the other is an exponential function.
The quadratic function f(x) will be
f(x) = ax² + bx + c
At x = 1, f(x) will be 3
a + b + c = 3 ...1
At x = 2, f(x) will be 6
4a + 2b + c = 6 ...2
At x = 3, f(x) will be 11
9a + 3b + c = 11 ...3
On solving equations 1, 2, and 3, we have
a = 1, b = 0, and c = 2
Then the quadratic function will be
f(x) = x² + 2
The exponential function g(x) will be given as
g(x) = abˣ
At x = 1, g(x) will be 3
ab = 3 ...4
At x = 2, g(x) will be 9
ab² = 9 ...5
From equations 4 and 5, we have
a = 1 and b = 3
Then the exponential function will be
[tex]\rm g(x) = 3^x[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
(2f-1)^2, please help, also tell me how to give you brainlyist, or what ever it’s called
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Answer:
4f^2 -4f +1
Step-by-step explanation:
It can be useful to memorize the form of the square of a binomial:
(a +b)^2 = a^2 +2ab +b^2
Here, you have a=2f and b=-1. Then the square is ...
(2f)^2 +2(2f)(-1) +(-1)^2 = 4f^2 -4f +1
__
More generally, the distributive property applies.
(2f -1)^2 = (2f -1)(2f -1) = 2f(2f -1) -1(2f -1)
= (2f)(2f) +(2f)(-1) +(-1)(2f) +(-1)(-1) = 4f^2 -2f -2f +1 = 4f^2 -4f +1
Which best describes the relationship between the lines with equations -36x + 8y = 16 and
-9x + 2y = 4?
Hi there! :)
Answer:
The lines are the same.
Step-by-step explanation:
Begin by converting each equation into its simplest form in slope-intercept form:
-36x + 8y = 16
Move the "x" variable to the right side of the equation:
8y = 36x + 16
Divide all terms by 8:
y = 36/8x + 16/8
y = 9/2x + 2
-------------------------------
-9x + 2y = 4
Move "x" variable:
2y = 9x + 4
Divide both sides by 2:
y = 9/2x + 2
Both of the equations are equivalent, meaning both of the lines are the same.
30) Luke has drawn a model figure as shown below to represent a garden he wishes to build. If he is planning on using a
scale factor of 2 cm: 5 ft, how long does the fence need to be?
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Answer:
45 ft
Step-by-step explanation:
The fence is shown as 18 cm, which is 9 times 2 cm. If 2 cm represents 5 ft, then the actual fence will be 9 times 5 ft = 45 ft.
- -
X+y=3 and x+y=-2 find the value of x and y
Answer:
no solutions.
Step-by-step explanation:
the given lines are parallel, then they can not have intersection points.
Dividing integers
7. (-154) ➗ (-14) =
11. (-40) ➗10=
15. 90 ➗ (-15)=
16. 108 ➗ (-9)=
17. (-48) ➗ (-6)=
18. (-105) ➗ 7=
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =11
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-4
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-6
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-616. 108 ➗ (-9)=-12
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-616. 108 ➗ (-9)=-1217. (-48) ➗ (-6)=8
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-616. 108 ➗ (-9)=-1217. (-48) ➗ (-6)=818. (-105) ➗ 7=-15
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-616. 108 ➗ (-9)=-1217. (-48) ➗ (-6)=818. (-105) ➗ 7=-15hope it helps you...........
Help me I’m stuck please
Answer:
choice 1,2,4,5 from top to bottom
Step-by-step explanation:
1:the points given are in the line where both planes intersect
2:point H is not on any plane
3:in the diagram point F is on plane R so false
4:if you connect the points given they will intersect so not collinear
5:the points F and G are on the plane R
6:so F is on plane R but H is not on any do false
What is the critical F value when the sample size for the numerator is seven and the sample size for the denominator is six
Answer:
Critical F value = 4.9503
Step-by-step explanation:
Given that:
The sample size of the numerator = 7
The sample size of the denominator = 6
The degree of freedom for the numerator df = n -1
The degree of freedom for the numerator df = 7 - 1
The degree of freedom for the numerator df = 6
The degree of freedom for the denominator df = n - 1
The degree of freedom for the denominator df = 6 - 1
The degree of freedom for the denominator df = 5
The assume that the test is two tailed and using a level of significance of ∝ = 0.10
The significance level for the two tailed test = 0.10/2 = 0.05
From the standard normal F table at the level of significance of 0.05
Critical F value = 4.9503
What is the intersection of the given lines? AB←→and EB←→ point B BE←→ point A point E
Answer:
point B
Step-by-step explanation:
The names of the lines, AB and BE, tell you that point B is on both lines.
Point B will be the point of intersection.
Answer:
point b
Step-by-step explanation:
i took the test and got it right
A B means:
A is an element of B
B is a subset of A
B is an element of B
A is a subset of B
none of the above
Answer:
A is a subset of B i believe that's the answer
Su Jean is driving from phoenix to houston. A distance of 1185 miles. After driving for 4 hours she calculates that she has driven 237 miles. What portion of the distance does she have left to drive?
Answer:
4/5
Step-by-step explanation:
237/1185 = .2 = 1/5
meaning there's 4/5 left
Which equation would represent 30 kittens divided into groups of 4
Answer:
30÷4
Step-by-step explanation:
Use technology to find the P-value for the hypothesis test described below. The claim is that for 12 AM body temperatures, the mean is F. The sample size is n and the test statistic is t.
Answer:
P value = 0.1575
Step-by-step explanation:
Data provided in the question
t = 1.021
n = 33
[tex]\mu[/tex] = 98.6° F
Based on the above information, the P-value could be determined by using the excel spreadsheet i.e. shown in the attachment
So, the P value is 0.1575
The 1.021 denotes the test statistic
32 denotes degrees of freedom
And,
1 denotes one tailed alternative hypothesis.
Credit card companies lose money on cardholders who fail to pay their minimum payments. They use a variety of methods to encourage their delinquent cardholders to pay their credit card balances, such as letters, phone calls and eventually the hiring of a collection agency. To justify the cost of using the collection agency, the agency must collect an average of at least $200 per customer. After a trial period during which the agency attempted to collect from a random sample of 100 delinquent cardholders, the 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75). Given this, what recommendation(s) would you make to the credit card company about using the collection agency
Answer with explanation:
A x% confidence interval interprets that a person can be x% confident thatthe true mean lies in it.
Here, Credit card companies is using the collection agency to justify the cost of , the agency must collect an average of at least $200 per customer.
i.e. [tex]H_0:\mu \geq200,\ \ \ H_a:\mu<200[/tex]
The 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75) .
I recommend that we can be 90% sure that the true mean collected amount lies in ($190.25, $250.75).
Also, $200 lies in it such that it is more far from $250.75 than $190.25, that means there are large chances of having an average is at least $200 per customer.
5 people cleared a plot of land in 15 days. How many people would I need to hire to clear three times that plot in 5 days?
Use AABC shown below to answer the question that follows:
Which of the following is a step towards proving the similarity of triangle so AABC and ADBA? (5 points)
Segment BC is a hypotenuse.
Angle B is congruent to itself.
Segment BA is shorter than segment BC.
Segment BC is intersected by segment AD.
Answer:
Bc is intersected by segment AD
Answer:
Bc is intersected by segment AD
Step-by-step explanation:
Find the slope of the line tangent to the graph of x²+2xy² +3y=31 at the point (2, -3)
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Answer:
22/21
Step-by-step explanation:
Taking the derivative, we have ...
2x·dx +2y²·dx +4xy·dy +3·dy = 0
dx(2x +2y²) +dy(4xy+3) = 0
At the given point, this is ...
dx(2·2 +2·(-3)²) +dy(4·2·(-3) +3) = 0
22dx -21dy = 0
dy/dx = 22/21
The slope of the tangent at the point of interest is 22/21.
a golfer hits the golf ball. the quadratic y = -14x^2+84x gives the time x seconds when the golf ball is at height 0 feet. In total, how long is the golf ball in the air?
Answer: 6 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) when the ball lands on the ground (y = 0)
0 = -14x² + 84x
0 = -14x(x - 6)
0 = -14x 0 = x - 6
0 = x 6 = x
x = 0 seconds is when the ball was hit
x = 6 seconds is when the ball landed on the ground
Please Hurry ...Which expression is equivalent to
Answer:
[tex]\huge\boxed{\sf \frac{160rs^5}{t^6}}[/tex]
Step-by-step explanation:
[tex]\sf 5r^6t^4 ( \frac{4r^3s^tt^4}{2r^4st^6} ) ^5[/tex]
Using rule of exponents [tex]\sf a^m/a^n = a^{m-n}[/tex]
[tex]\sf 5r^6t^4 ( 2 r^{3-4} s^{2-1}t^{4-6})^5\\5r^6t^4(2r^{-1}st^{-2})^5\\5r^6t^4 * 32 r^{-5}s^5t^{-10}[/tex]
Using rule of exponents [tex]\sf a^m*a^n = a^{m+n}[/tex]
[tex]\sf 160 r^{6-5}s^5t^{4-10}[/tex]
[tex]\sf 160 rs^5 t^{-6}[/tex]
To equalize the negative sign, we'll move t to the denominator
[tex]\sf \frac{160rs^5}{t^6}[/tex]