Answer:
d) [tex]8.97*10^{-3}[/tex]
Step-by-step explanation:
Move the decimal 3 spaces to the right so that way the decimal can be between the first two numbers. When you move the decimal to the right, it makes the exponent negative, when it moves to the left, it makes it positive
The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 46 who smoke.
Step 1 of 2: Suppose a sample of 2172 Americans over 46 is drawn. Of these people, 1738 don't smoke. Using the data, estimate the proportion of Americans over 46 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places.
The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 46 who smoke.
Step 2 of 2: Suppose a sample of 2172 Americans over 46 is drawn. Of these people, 1738 don't smoke. Using the data, construct the 98 % confidence interval for the population proportion of Americans over 46 who smoke. Round your answers to three decimal places
Answer:
1.) .800
2.).779 to .821
Step-by-step explanation:
We must assume that the sample that we are given to work with is representative of the population, in which case we just need to find the proportion of people in the sample who don't smoke. This is [tex]\frac{1738}{2172}[/tex] = .8002, or .800 rounded to three decimal places.
Part 2 will build off the answer in step 1. The middle of the confidence interval will be the estimate gained from the sample, or .800. The critical value of 98% equals 2.326 when using the normal model. The standard deviation can be calculated using the formula [tex]\sqrt{\frac{(proportion)(1-proportion)}{n} }[/tex]. Plugging in the numbers you get [tex]\sqrt{\frac{(.8)(.2)}{2172} }[/tex]= .009.
This means the confidence interval is .800±.021
4. Factor the expression.
4b2 + 28b + 49
QA (2b + 7)2
OB (2b - 72
C (-2b + 7)2
OD 2(b - 7)2
Answer:
A. [tex](2b+7)^2[/tex]
Step-by-step explanation:
[tex]4b^2 +28b + 49\\=(2b)^2 + 2\times 2b\times 7 + (7)^2\\=(2b+7)^2[/tex]
The sum of the 3rd term and 4th term of an arithmetic sequence is 18. The 7th term exceeds the 5th term by 14. Find the first term and common difference.
Answer:
First term = -8.5.
Common difference = 7.
Step-by-step explanation:
The third term = a1 + 2d where a1 = first term and d is the common difference so we have
a1 + 2d + a1 + 3d = 18
2a1 + 5d = 18............(1)
Also:
7th term - 5th term = 14 giving
a1 + 6d - ( a1 + 4d) = 14
2d = 14
d = 7.
So the common difference is 7 and substituting for d in (1) we have:
2a1 + 5*7 = 18
2a1 = 18-35 = -17
a1 = -8.5.
The first term and the common difference of the sequence are -8.5 and 7 respectively.
The sum of the 3rd term and 4th term of an arithmetic sequence is 18.
Using Arithmetic progression formula,
aₙ = a + (n- 1)d
where
n = nth term
a = first term
d = common difference
a₃ = a + 2d
a₄ = a + 3d
Therefore,
a + 3d + (a + 2d) = 18
2a + 5d = 18
The 7th term exceeds the 5th term by 14. Therefore,
a₅ = a + 4d
a₆ = a + 6d
a + 6d - (a + 4d) = 14
a + 6d - a - 4d = 14
2d = 14
d = 14 / 2
d = 7
2a + 5d = 18
2a + 5(7) = 18
2a + 35 = 18
2a = 18 - 35
2a = -17
a = -17 / 2
a = -8.5
learn more on arithmetic progression here: https://brainly.com/question/18494472?referrer=searchResults
Identify three misconception each of any five topic's in mathematics
62 = 12.
7 x 0 = 7.
Four hundred and eight is written as 4008.
0.10 = point ten.
0.5 x 10 = 0.50.
6 -:- ½ = 3.
- 5 + 3 = -8.
4% is 0.4 as a decimal.
Evaluate 3(6-14) over -4
Answer:
-6
Step-by-step explanation:
(3 x 6) - (3 x 14)
= 18 - 42
= -24
-24/4
= -6
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
problem decoded dude
first follow meh and then thank me
My name is Jerry
Consider the polynomials Bold p 1 (t )p1(t) equals = 3 3 plus + 8 8t, Bold p 2 (t )p2(t) equals = 3 3 minus − 8 8t, and Bold p 3 (t )p3(t) equals = 6 6 (for all t). By inspection, write a linear dependence relation among Bold p 1 p1, Bold p 2 p2, and Bold p 3 p3. Then find a basis for Span StartSet Bold p 1 comma Bold p 2 comma Bold p 3 EndSet Spanp1, p2, p3.
Answer:
Apparently [tex]\mathbf{p}_1(t) + \mathbf{p}_2(t) - \mathbf{p}_3(t) = 0[/tex].
One possible basis for this span is [tex]\left\{3 + 8\, t,\, 3 - 8\, t\right\}[/tex].
Step-by-step explanation:
Linear DependenceA set of vectors is linearly-dependent if one of the vectors is a linear combination of the others.
Alternatively, to show linear dependence, show that the equation [tex]a\, \mathbf{p}_1 + b\, \mathbf{p}_2 + c\, \mathbf{p}_3 = 0[/tex] has a non-trivial solution (where at least one of the three scalars [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] is non-zero.)
For this set of polynomials, it can be shown that:
[tex]\mathbf{p}_3(t) = \mathbf{p}_1(t) + \mathbf{p}_2(t)[/tex], or equivalently,
[tex]\mathbf{p}_1(t) + \mathbf{p}_2(t) - \mathbf{p}_3(t) = 0[/tex].
Either way, the set [tex]\left\{\mathbf{p}_1,\, \mathbf{p}_2,\, \mathbf{p}_3\right\}[/tex] would be linearly-dependent.
Basis of the Span[tex]\mathbf{p}_3(t) = \mathbf{p}_1(t) + \mathbf{p}_2(t)[/tex] implies that [tex]\mathbf{p}_3[/tex] is a linear combination of [tex]\mathbf{p}_1[/tex] and [tex]\mathbf{p}_2[/tex]. Therefore, [tex]\mathbf{p}_3[/tex] is in the span of [tex]\mathbf{p}_1[/tex] and [tex]\mathbf{p}_2[/tex] (in other words, [tex]\mathbf{p}_3 \in \mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2\right\}[/tex].) Hence:
[tex]\mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2,\, \mathbf{p}_3\right\} = \mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2\right\}[/tex].
Therefore, any basis of the set [tex]\mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2\right\}[/tex] would also be a basis of the set [tex]\mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2,\, \mathbf{p}_3\right\}[/tex].
On the other hand, it can be shown that [tex]\mathbf{p}_1[/tex] and [tex]\mathbf{p}_2[/tex] are linearly-independent. Therefore, [tex]\mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2\right\}[/tex] should have a dimension of [tex]2[/tex]. As a result, there should be exactly [tex]2[/tex] linearly-independent vectors in a basis of [tex]\mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2\right\}[/tex].
There are many different choices for the basis of [tex]\mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2\right\}[/tex]. One possible choice is the set [tex]\left\{\mathbf{p}_1,\, \mathbf{p}_2\right\}[/tex], which is equal to [tex]\left\{3 + 8\, t,\, 3 - 8\, t\right\}[/tex]. Make sure that this set is indeed linearly-independent and contains two vectors.
Because it has already been shown that [tex]\mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2,\, \mathbf{p}_3\right\} = \mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2\right\}[/tex], [tex]\left\{3 + 8\, t,\, 3 - 8\, t\right\}[/tex] should be a basis of the set [tex]\mathrm{Span}\left\{\mathbf{p}_1,\, \mathbf{p}_2,\, \mathbf{p}_3\right\}[/tex], as well.
If the radius of a circle is 31.2 cm, what is the approximate area if you use 3.14 for pi and the area is rounded to the nearest tenth?
Answer:
3056.6 cm^2
Step-by-step explanation:
A = (pi)r^2 = 3.14 * 31.2 cm * 31.2 cm = 3056.6 cm^2
Answer: 3056.60 sq. cm.
Step-by-step explanation:
Area of a circle = π x r^2
= 3.14 x 31.2^2
= 3056.60
Troy starts to construct a triangle congruent to right
isosceles triangle ABC. He begins by constructing a
perpendicular through a point not on a line, as shown.
D
Use the drop-down menus to complete the additional
steps needed to finish the congruent triangle
construction.
Place the compass center at C and set the radius to
the length of CB. Because
he needs to
set the compass radius only once.
Keeping the compass width the same, move the
compass center to F and draw arcs to intersect
segments
The points where the arcs intersect the segments are
the of the triangle. Construct segments to
form the remaining sides of the triangle.
А
F
E
с
B
H
Answer:
CB=CA
FD and FG
Verticies
Step-by-step explanation:
Answer:
B,A,C
Step-by-step explanation:
because Place the compass center at C and set the radius to
the length of CB. Because
he needs to
set the compass radius only once.
Keeping the compass width the same, move the
compass center to F and draw arcs to intersect
segments
The points where the arcs intersect the segments are
the of the triangle. Construct segments to
form the remaining sides of the triangle
Phil has $20,000, part of which he invests at 8% interest and the rest at 6%. If the total income from the two investments was $1460, how much did he invest at 6%?
Answer: 7000
Step-by-step explanation:
Let the amount invested in 8% account be P1 and the amount invested in 6% account be P2
. If the total amount invested is $20,000 then:
P1+P2=20,000. (Eq. 1)
The interest earned in one year from the 8% account is:
I1=0.08P1
and the interest earned in one year from the 6% account is:
I2=0.06P2
If the total interest earned is $1460, then:
I1+I2=1460
0.08P1+0.06P2=1460
(Eq. 2) From Eq. 1 :
P1=20000−P2
Substituting this into Eq. 2:
0.08 (20000−P2) + 0.06P2 = 1460
1600 − 0.08P2 + 0.06P2 = 1460
0.02P2 = 140
P2 = 140 / 0.02
P2 = 7000
Hence, he invested $7000 at the rate of 6%.
six more than the product of nine and a number Evaluate when q = 6
Answer:
60
Step-by-step explanation:
Let's name "a number" "q."
The expression we can set up is 6+9q
Plug 6 in for q.
6+9(6)
6+54
60
What is the additive inverse of the complex number 9-412
-9-41
-9 +41
9 - 41
9 + 41
Additive inverse means the sum should be 0
so all you gotta do is multiply the complex number by -1
(the question isn't clear so I can't state the option)
how to simplify 2x^2 - 18 =0
Answer:
X=3 or x= -3
Step-by-step explanation:
2x^2 - 18 =0
Take a common factor
2(x^2 - 9) = 0
2(x-3)(x+3)=0
X-3=0 or x+3=0
X=3 x=-3
Hope this helps!
Step-by-step explanation:
Hope this is correct
HAVE A GOOD DAY!
According to a Pew Research Center, in May 2011, 35% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.She selects 300 community college students at random and finds that 120 of them have a smart phone. In testing the hypotheses: H0: p = 0.35 versus Ha: p > 0.35, she calculates the test statistic as Z = 1.82.1. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).2. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.068).3. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.966).4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034)
Answer:
Step-by-step explanation:
For the null hypothesis,
p = 0.35
For the alternative hypothesis,
P > 0.35
Since the z score is given as z = 1.82, we would find the probability value by determining the area above the z score from the normal distribution table. The required probability value is
1 - 0.966 = 0.034
Assuming alpha = 0.05,
Since alpha, 0.05 > than the p value, 0.034, then we would reject the null hypothesis. Therefore, the correct option is
At significance level of 5%,
There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
iven two dependent random samples with the following results: Population 1 70 60 72 55 69 50 55 74 Population 2 72 56 81 50 79 60 50 78 Can it be concluded, from this data, that there is a significant difference between the two population means? Let d=(Population 1 entry)−(Population 2 entry). Use a significance level of α=0.1 for the test. Assume that both populations are normally distributed. Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.
Answer:
The value of the test statistic is:
t = -1.112
Step-by-step explanation:
In this case a paired difference test is to be performed.
The hypothesis can be defined as follows:
H₀: There is no difference between the two population means, i.e. d = 0.
Hₐ: There is a significant difference between the two population means, i.e. d ≠ 0.
The significance level of the test is, α = 0.10.
Use MS-Excel to perform the analysis.
Consider the output attached below.
The value of the test statistic is:
t = -1.112
The p-value of the two-tailed test is:
p-value = 0.303.
Decision rule:
Reject the null hypothesis if the p-value is less than the significance level.
p-value = 0.303 > α = 0.10.
The null hypothesis was failed to be rejected at 10% level of significance.
Conclusion:
There is not enough evidence to support the claim that there is a difference between the two population means.
The function f(x)= 200/X+ 10 models the cost per student of a field trip when x students go on the trip. How is the parent function
f(x) = 1/x transformed to create the function f(x)= 200/x + 10
O It is vertically stretched by a factor of 200.
O It is vertically stretched by a factor of 200 and shifted 10 units leftt
O It is vertically stretched by a factor of 200 and shifted 10 units up.
O It is vertically stretched by a factor of 200 and shifted 10 units right
Answer:
It is vertically stretched by a factor of 200 and shifted 10 units right
Step-by-step explanation:
Suppose we have a function f(x).
a*f(x), a > 1, is vertically stretching f(x) a units. Otherwise, if a < 1, we are vertically compressing f(x) by a units.
f(x - a) is shifting f(x) a units to the right.
f(x + a) is shifting f(x) a units to the left.
In this question:
Initially: [tex]f(x) = \frac{1}{x}[/tex]
Then, first we shift, end up with:
[tex]f(x+10) = \frac{1}{x + 10}[/tex]
f was shifted 10 units to the left.
Finally,
[tex]200f(x+10) = \frac{200}{x + 100}[/tex]
It was vertically stretched by a factor of 200.
So the correct answer is:
It is vertically stretched by a factor of 200 and shifted 10 units right
Answer:
the answer is D
Step-by-step explanation:
find the quotient of (5+4i)/(6+8i) ans express in simplest forms
Answer:
Your correct answer is 31/50 + -4/25 i
Step-by-step explanation:
5+4i/6+8i = 31/50 + -4/25 i
subtract 8 1/6 - 5 1/8
Answer:
3 1/24
(Decimal: 3.041667)
hope i helped
-lvr
Answer:
3 1/24
Step-by-step explanation:
8 1/6 - 5 1/8
Get a common denominator of 24
8 1/6 *4/4 - 5 1/8*3/3
8 4/24 - 5 3/24
3 1/24
Which are the right ones?
Answer:
20 4/5
Step-by-step explanation:
13/5 times 8/1
104/5
which is simplify
to 20 4/5\
hope this helps
An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion p is less than 0.10, he will reject the shipment. He will test the hypotheses H0: p = 0.10, Ha: p < 0.10. He selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Suppose that 12 of the potatoes sampled are found to have major defects. The P-value of this test is:
Answer:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.06-0.10}{\sqrt{\frac{0.10(1-0.10)}{200}}}=-1.89[/tex]
And the p value would be given by:
[tex]p_v =P(z<-1.89)=0.0294[/tex]
Step-by-step explanation:
Information given
n=200 represent the random sample taken
X=12 represent the potatoes with major defects
[tex]\hat p=\frac{12}{200}=0.06[/tex] estimated proportion of potatoes with major defects
[tex]p_o=0.10[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true proportion is less than 0.10 so then the system of hypothesis are:
Null hypothesis:[tex]p\geq 0.1[/tex]
Alternative hypothesis:[tex]p < 0.10[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.06-0.10}{\sqrt{\frac{0.10(1-0.10)}{200}}}=-1.89[/tex]
And the p value would be given by:
[tex]p_v =P(z<-1.89)=0.0294[/tex]
Considering the hypothesis tested, the p-value is of 0.0294.
The null hypothesis is:
[tex]H_0: p = 0.1[/tex]
The alternative hypothesis is:
[tex]H_a: p < 0.1[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are:
[tex]p = 0.1, n = 200, \overline{p} = \frac{12}{200} = 0.06[/tex]
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.06 - 0.1}{\sqrt{\frac{0.1(0.9)}{200}}}[/tex]
[tex]z = -1.89[/tex]
The p-value for this test is the probability of finding a sample proportion of 0.06 or below, which is the p-value of z = -1.89.
Looking at the z-table, z = -1.89 has a p-value of 0.0294.A similar problem is given at https://brainly.com/question/24166849
Which numbers are solutions to the inequality
-3x-3 less than or equal to 6. Check all of the boxes that apply.
-5
-4
0
2
4
The values greater than -3, such as 0, 2, and 4 are solutions to the inequality.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
-3x-3 less than or equal to 6
This can be written as -3x-3≤6
Add 3 on both the sides
-3x≤6+3
-3x≤9
Divide both sides by 3
-x≤3
x≥-3
Hence, the values greater than -3, such as 0, 2, and 4 are solutions to the inequality.
To learn more on Inequality click:
https://brainly.com/question/28823603
#SPJ2
Answer: 0,2,4
Step-by-step explanation:
just did the test
what is the greatest possible prime you must consider to test whether 8243 is prime?
Answer:
I'll consider just 3
Step-by-step explanation:
To check if a number is a prime number it has to undergo series of division.
Let's not forget that a prime number is a number divisible by only itself and one
So for my argument.
2 cannot the number
3 cannot also divide the number
5 and 7 too cannot Divide the number.
I'll consider just 3 as the highest prime number to divide it
If f(x) = 6 - 5x, what is f(x)^-1? (check attachment)
f(x) = 6-5x
y = 6-5x .... replace f(x) with y
x = 6-5y .... swap x and y; solve for y
x+5y = 6
5y = 6-x
y = (6-x)/5
[tex]f^{-1}(x) = \frac{6-x}{5}[/tex] ... replace y with the inverse function notation
Answer: Choice D.What is the sampling method used in the following scenario? The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
Answer:
Step-by-step explanation:
The method applied in this scenario is called simple random sampling. A sample of 100 customers is chosen from a larger population of customers and each customer has the same chance of being selected for the survey at any given time. Also, the chance of selecting 100 customers from each store is the same during the sampling process. The order of sampling at each store does not follow a certain order, thus, It is different from systematic random sampling.
A laptop computer is purchased for $2300. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth $700 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.
Answer:
after the 1st year
Step-by-step explanation:
$2300 × 75% = $1725.00
$2300-$1725= $575
help me please please
Answer:
3.88 nm
Step-by-step explanation:
The angle at Port Latta between the actual direction of travel and the destination at Lookout Point is 90° -75° = 15°. The sine function relates the angle, the side opposite, and the hypotenuse of a right triangle, so you have ...
sin(15°) = (distance to Lookout Point)/(15 nm)
Solving for the desired distance, we have ...
distance to Lookout Point = (15 nm)sin(15°) = 3.88 nm
The yacht is 3.88 nautical miles from Lookout Point.
Use Green’s Theorem to evaluate the line integral along the given positively oriented curve. ∫c cos y dx + x^2 sin y dy, C is the rectangle with vertices (0, 0), (5, 0), (5, 2), and (0, 2)
By Green's theorem, we have
[tex]\displaystyle\int_C\cos y\,\mathrm dx+x^2\sin y\,\mathrm dy=\iint_R\frac{\partial(x^2\sin y)}{\partial x}-\frac{\partial\cos y}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]
where [tex]C[/tex] is the *boundary* of the rectangle [tex]R[/tex].
The integral is then
[tex]\displaystyle\int_0^5\int_0^2(2x+1)\sin y\,\mathrm dy\,\mathrm dx[/tex]
[tex]=\displaystyle(\cos0-\cos2)\int_0^5(2x+1)\,\mathrm dx[/tex]
[tex]=\displaystyle(1-\cos2)(5^2+5)=\boxed{30(1-\cos 2)}[/tex]
Your class built a tepee to use in the school play. The tepee has a diameter of 16 feet and a height of 13.5 feet. What is the volume? Use 3.14 for pi. Round your answer to the nearest whole number.
Answer:
904.78
Step-by-step:
V=πr2h
3=π·82·13.5
3≈904.77868
Hope this helps
Question 5(Multiple Choice Worth 1 points)
(02.05 MC)
Given the function f(x) = 3x + 1 and the linear function g(x), which function has a greater value when x = 3?
Answer:
g(x) is greater
Step-by-step explanation:
Which transformations could have occurred to map AABC
to AA"B"C"?
O a rotation and a dilation
O a rotation and a reflection
O a reflection and a dilation
O a translation and a dilation
Answer:
A reflection and a dialation
Step-by-step explanation:
Reflection is when you flip a figure over a line. Rotation is when you rotate a figure a certain degree around a point. Dilation is when you enlarge or reduce a figure.In this case a rotation is not nessasary, so I would suggest a reflection in the y-axis and a dialation to shrink the triangle to A'B'C'
So for the transformations that could have occurred to map ABC to A'B'C' you should choose the answer
a reflection and a dialation
The transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation
Key Facts on TransformationsReflection is simply flipping a shape over an axis.Dilation means enlarging a figure or reducing the size of a figure.Rotation simply involves rotating a figure around a given point while maintaining same size.Translation is shifting the points of a figure to move it to another position.Thus, in the transformation shown, figure ABC was reflected over the y-axis and then dilated to give A'B'C'.
Therefore, the transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation
Learn more about transformation on:
https://brainly.com/question/1462871
