Answer:
-1/10 , 0, and 1/10
Step-by-step explanation:
1/8 > x > -1/7
Where x is a rational number.
-1/10 is rational.
0 is rational.
1/10 is rational.
Erin gets her exercise by running. The graph shows the distances she covers in a given amount of time. How many hours does it take for Erin to run 25 miles?
Answer:
2½ h
Step-by-step explanation:
Assume the graph is like the one below.
The graph shows how Erin's distance varies with time.
To find out how long it takes Erin to cover 25 mi, find 25 mi on the vertical axis.
From there, draw a horizontal line until it hits the graph.
Then drop a vertical line to the horizontal axis.
It hits half-way between 2 and 3.
It takes Erin 2½ h to run 25 mi.
Answer:
2½ h
Step-by-step explanation:
A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over the age of 55, 68 dream in black and white and among 288 people under the age of 25, 19 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those underIdentify the test statistic?Identify the p value?Test the claim by constructing an appropriate confidence level?What is the conclusion base on the hypothesis test?What is the conclusion base on the confidence level?
Answer:
he proportion of people over 55 who dream in black and white is greater than the proportion of those under.
The proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).
Step-by-step explanation:
In this case we need to determine if the proportion of people over 55 who dream in black and white is greater than the proportion of those under.
The hypothesis can be defined as follows:
H₀: The proportion of people over 55 who dream in black and white is not greater than the proportion of those under, i.e. p₁ - p₂ ≤ 0.
Hₐ: The proportion of people over 55 who dream in black and white is greater than the proportion of those under, i.e. p₁ - p₂ > 0.
The information provided is:
n₁ = 290
n₂ = 288
X₁ = 68
X₂ = 19
Compute the sample proportions and total proportions as follows:
[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{68}{290}=0.235\\\\\hat p_{2}=\frac{X_{2}}{n_{1}}=\frac{19}{288}=0.066\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{68+19}{290+288}=0.151[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.235-0.066}{\sqrt{0.151(1-0.151)[\frac{1}{290}+\frac{1}{288}]}}\\\\=5.67[/tex]
The test statistic value is 5.67.
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=P(Z>5.67)\\=1-P(Z<5.67)\\=1-\approx1\\=0[/tex]
The p-value of the test is quite small.
The null hypothesis will be rejected at 5% significance level.
Thus, the proportion of people over 55 who dream in black and white is greater than the proportion of those under.
The significance level of the test is 5%.
Then the confidence level will be:
Confidence level = 100% - Significance level
= 100% - 5%
= 95%
Compute the 95% confidence interval for the difference between proportions as follows:
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]
The critical value of z for 95% confidence level is z = 1.96.
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]
[tex]=(0.235-0.066)\pm1.96\cdot\sqrt{\frac{0.235(1-0.235)}{290}+\frac{0.066(1-0.066)}{288}}\\\\=0.169\pm 0.057\\\\=(0.112, 0.226)[/tex]
The null hypothesis would be rejected if the null value, i.e. (p₁ - p₂) ≤ 0 is not contained in the interval.
The 95% confidence interval consist of values greater than 0.
Thus, the null hypothesis will be rejected.
Concluding that the proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).
next,you will make a scatter plot. Name a point that will be on your scatterplot and describe what it represents.
Answer:
(12, 190). This represents that after selling 12 ice creams, I gain $190.
Step-by-step explanation:
I just found a scatter plot online. Ignore the current label on the x-axis that says TemperatureC, I just changed that to ice creams. You can change the title of the graph to whatever you want.
SOME PLEASE HELP WITH THE ANSWER!!! Thank you
Answer:
Geometric
Ratio
10:1
Step-by-step explanation:
The sequence is geometric because the common connection between the numbers is divided by 10.
It is ratio, because the sequence is geometric
The ratio is 10:1, because the previous number is 10 times as large as the following number
Hope this helps
classify the triangle according to its SIDES and ANGLES.
Answer:
this is a right angled triangle
Step-by-step explanation:
It has a 90 degree angle
the hypotenuse is the longest
The other two sides adjacent to the right angle are perpendicular
It could also be called an isosceles right angled triangle
Answer:
Right angled and Isosceles
Step-by-step explanation:
Right angled because one corner of the triangle is marked with a square, which shows it is 90degrees.
Isosceles because 2 angles and 2 sides have been marked with similar lines and curves, which shows that they are equal in length. When 2 angles and 2 sides are equal, the triangle is isosceles.
Hope this helps.
Good Luck
Please help! For all values of x, F(x)= x-1 And G(x)=2x^2+3 Solve fg(x)= gf(x)
Answer:
[tex]\boxed{\sf \ \ \ x=\dfrac{3}{4} \ \ \ }[/tex]
Step-by-step explanation:
hello,
f(x)=x-1
[tex]g(x)=2x^2+3[/tex]
so
[tex]fog(x)=f(g(x))=f(2x^2+3)=2x^2+3-1=2x^2+2 \ and \\gof(x)=g(f(x))=g(x-1)=2(x-1)^2+3=2x^2-4x+2+3=2x^2-4x+5 \ \ So\\\fog(x)=gof(x) <=>2x^2+2=2x^2-4x+5\\<=>4x=5-2=3\\<=>x=\dfrac{3}{4}[/tex]
hope this helps
[tex]\frac{3}{4}[/tex]
The composition of a function is a process in which two functions [tex]f,g[/tex], are combined to produce a new function, [tex]h[/tex], with the formula [tex]h(x)=g(f(x))[/tex]. It means that the [tex]g[/tex] function is being applied to the [tex]x[/tex] function.
[tex]f(x)=x-1\\g(x)=2x^2+3[/tex]
[tex]f(g(x))=f(2x^2+3)[/tex]
[tex]=2x^2+3-1\\=2x^2+2[/tex]
[tex]g(f(x))=g(x-1)[/tex]
[tex]=2(x-1)^2+3\\=2x^2+2-4x+3\\=2x^2-4x+5[/tex]
[tex]f(g(x))=g(f(x))[/tex]
[tex]2x^2+2=2x^2-4x+5[/tex]
[tex]4x=3[/tex]
[tex]x=\frac{3}{4}[/tex]
For more information:
https://brainly.com/question/12431044?referrer=searchResults
What is the length of XQY?
Answer:
88
Step-by-step explanation:
First you must find the circumference of the entire circle and to do this you use 2πr. The radius in this case is PX=15. This means that the circumference is 30π. Now to find the arc length, we know that the measure of arc XY is 23 degrees, and since there are 360 total degrees in a circle, we must subtract 23 from 360 to get 337° as the measure of arc XQY. Now we have to find what portion of the circumference of the circle is in this arc, and to do this you divide the arc length (337°) by 360° and multiply by the circumference of the circle. Doing this would get you [tex]\frac{337}{360} *30\pi[/tex] which equals ~28. Finally, you have to multiply this by the value of pi and get approximately 88, which is your answer.
What is an equation of the line that is perpendicular to y=−34x+6 and passes through the point (3, 9)?
Answer:
y = 4/3x + 5
Step-by-step explanation:
if the slope is -3/4 then the perpendicular slope is 4/3
y = mx + b
9 = 4/3(3) + b
9 = 4 + b
5 = b
y = 4/3x + 5
Classify each situation as exponential growth or exponential decay.
Answer:
Step-by-step explanation:
Exponential Growth:
1). The value of a home in a growing community every year.
2). The amount of money in a saving account that earns interest annually.
Exponential decay:
1). The monthly sale of albums of a band whose popularity is declining.
2). The amount of radioactive element remaining in a sample every decade.
3). The temperature of a hot cup of coffee left on the counter every minute.
in a survey of 9000 people, 4000 likes tea,4500 like coffee. among them 2500 dont like tea and coffee. find number of people who like tea and coffee both
Step-by-step explanation:
No of people likes tea = 4000
No of people like coffee = 4500
Total = 8500
No of people don't like tea and coffee = 2500
No of people like tea and coffee = 8500 - 2500 = 6000
Answer:
500
Step-by-step explanation:
n(t)=4000
n(c)=4500
n(tea only )= 4000-x
n(coffee only )= 4500-x
n(coffee and tea )= x
note...using Venn diagram ..all together must add up to 9000
(4000-x)+(4500-x) +x = 9000
..............
...........collect like terms
9500-9000 = x
x = 500
Sue has 20 biscuits in a tin. there are: 12 plain biscuits 5 chocolate biscuits 3 currant biscuits. sue takes at random two biscuits from the tin. work out the probability that the two biscuits were not the same.
Answer:
58.43%
Step-by-step explanation:
In this case we have that the probability that they are different is the opposite of the probability that they are the same, therefore, in each case it would be:
P (plain, plain) = (12/20) (11/19)
P (p, p) = 132/380
P (chocolate, chocolate) = (5/20) (4/19) = 20/380
P (ch, ch) = 20/380
P (currant, currant)= (3/20) (2/19) = 6/380
P (c, c) = 6/380
The probability that they are equal is the sum of each:
P (equal) = 132/380 + 20/380 + 6/380
P (equal) = 0.4157
Therefore, the probability that they are different is:
P (different) = 1 - 0.4157
P (different) = 0.5843 = 58.43%
It means that the probability is 58.43%
Answer:111/190
Step-by-step explanation:
which equation describes this line? A. y-3=2(x-2) B. y-9=2(x-1) C. y-1=2(x-9) D. y-2=2(x-3)
Answer:
y = 2x + 7
Step-by-step explanation:
Step 1: Find slope
m = (9 - 3)/(1 + 2)
m = 2
y = 2x + b
Step 2: Find b
9 = 2(1) + b
9 = 2 + b
7 = b
Step 3: Rewrite equation
y = 2x + 7
Answer:
B) y - 9 = 2(x - 1)
Step-by-step explanation:
(-2, 3) ;(1,9)
[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{9-3}{1-[-2]}\\\\=\frac{6}{1+2}\\\\=\frac{6}{3}\\\\=2[/tex]
(1, 9 ) ; m = 2
Equation: [tex]y - y_{1}=m(x - x_{1})\\\\[/tex]
y - 9 = 2(x - 1)
y - 9 = 2x -2
y = 2x - 2 + 9
y = 2x + 7
Idek the answer, can someone help me pls
Answer:
A) 1/6
Step-by-step explanation:
There are six sides on a dice and one number 3.
That means that you have a chance in one of six roles to get a 3 one time.
This may not be very clear so you can ask more questions in the comments!
3x^2 Type of expression coefficients and constant
Answer & Step-by-step explanation:
3x²
This term represents a monomial expression. Mono- means one. This term is by itself. It has no other term added or subtracted to it.
The coefficient of this term is 3 because it is the number that the variable is connected to.
There are no constants because this is a monomial expression.
URGENT HELP PLEASE!
Solve the following equations on the interval 0<=x<=2pi
a) square root2 sin 2x=1
b) csc^2x-cscx-2=0
Answer:
(a) [tex]x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}[/tex]
(b) [tex]x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex]
Step-by-step explanation:
It is given that [tex]0\leq x\leq 2\pi[/tex].
(a)
[tex]\sqrt{2}\sin 2x=1[/tex]
[tex]\sin 2x=\dfrac{1}{\sqrt{2}}[/tex]
[tex]\sin 2x=\dfrac{\pi}{4}[/tex]
[tex]2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}[/tex] [tex][\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny][/tex]
[tex]x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}[/tex]
(b)
[tex]\csc^2 x-\csc x-2=0[/tex]
[tex]\csc^2 x-2\csc x+\csc x-2=0[/tex]
[tex]\csc x(\csc x-2)+1(\csc x-2)=0[/tex]
[tex](\csc x+1)(\csc x-2)=0[/tex]
[tex]\csc x=-1\text{ or }\csc x=2[/tex]
[tex]\sin x=-1\text{ or }\sin x=\dfrac{1}{2}[/tex] [tex][\because \sin x=\dfrac{1}{\csc x}][/tex]
[tex]x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex]
Therefore, [tex]x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex].
The state tax rate on 1973 incomes was 2% on the first $1000 of income subject to tax and 3% on the next $2000 or any part thereof. By special law, the State allowed a deduction of 1/4 of the tax computed on the above schedule. In 1973, $1800 of Mr. Brown's income was subject to tax. What was the amount of his tax? A) $11 B) $27 C) $33 D) $9
Answer: C) $33
Step-by-step explanation:
1973 tax rate :
2% on the first $1000 income
3% on next $2000 or any part thereof ;
Brown's total income of $1800
2% of $1000
0.02 × $1000 = $20
3% of $800
0.03 × 800 = $24
Total tax = $(20 + 24) = $44
1/4 tax deduction:
(1/4) of total tax
(1/4) × $44
0.25 × $44
= $11
Total tax - tax deduction
$44 - $11 = $33
Tax amount = $33
Someone help me do this? For math
Answer:
1, 4, 5, 7, 8
Step-by-step explanation:
once you plot the points you will see that these coordinates are inside the star
Pick all that apply the option answer in two minutes
Answer: PQT and TUV
Step-by-step explanation:
Can anyone pls solve this.
Answer:
3) [tex]\frac{(25)^{3/2} * (243)^{3/5}}{(16)^{5/4}*(8)^{4/3}}[/tex]
=> [tex]\frac{(5^2)^{3/2}*(3^5)^{3/5}}{(2^4)^{5/4}*(2^3)^{4/3}}[/tex]
=> [tex]\frac{5^3*5^3}{2^5*2^4}[/tex]
=> [tex]\frac{5^6}{2^9}[/tex]
4) [tex]\frac{3-2\sqrt{2} }{3+2\sqrt{2} }[/tex]
Multiplying and dividing by conjugate [tex]3-2\sqrt{2}[/tex]
=> [tex]\frac{(3-2\sqrt{2})(3-2\sqrt{2}) }{(3+2\sqrt{2})(3-2\sqrt{2})}[/tex]
=> [tex]\frac{9-6\sqrt{2}-6\sqrt{2} +8 }{9-8}[/tex]
=> [tex]\frac{17-12\sqrt{2} }{1}[/tex]
=> [tex]17-12\sqrt{2}[/tex]
Comparing it with [tex]a+b\sqrt{2}[/tex], we get
a = 17, b = -12
A cylindrical tank has a diameter of 2.5 feet and a height of 4.8 feet. what is the lateral surface area of the tank to the nearest hundredth square foot?
Answer:
This is approximately [tex]37.7 ft^{2}[/tex] to the nearest hundredth
Step-by-step explanation:
First of all, we will need to understand that to find the lateral surface area of the cylinder, we simply need to multiply the circumference of the circular base by the height of the cylinder.
In this case, the circumference of the circular base can be obtained by the formula
[tex]2 \pi r[/tex]
Hence we will have the circumference as [tex]2 \times \pi \times \frac{2.5}{2}=7.85 feet[/tex]
Tp get the Lateral area, we will simply have to multiply this value (7.85 feet )
by the height (4.8 feet)
7.85 X 4.8 =[tex]37.68 feet ^{2}[/tex]
This is approximately [tex]37.7 ft^{2}[/tex] to the nearest hundredth
picture is the qestion
Answer:
x = 12
Step-by-step explanation:
We can use the Cross Products Property.
9 / 12 = x / 16
12x = 9 * 16
x = 9 * 16 / 12 = 12
Answer:
x = 12
Step-by-step explanation:
→ First we work out the multiplier between 16 and 12 so,
16 ÷ 12 = 1.3 recurring
→ Multiply this multiplier by 9
9 × 1.3 recurring = 12
→ x = 12
A paper cup is a perfect cylinder that is 6.4 cm tall and 3 cm across. Find the total area of paper needed to make the cup, to the nearest square centimeter.
Hey there! I'm happy to help!
We want to find how much paper we need to make the cup. So, we need to find the surface area of the cylinder, which is basically the "walls and floors" of the cup. So, this is the circle on the bottom and the surrounding stuff that goes up. There is no circular top to this cup, which will be important when finding the total area of paper.
So, first we need to find how much paper we need to make the bottom circle. The formula for the area of a circle is A=πr². This r represents the radius, or the distance from the center of the circle to the edge. We are given that the cup is 3 cm completely across, and the radius is be half of that, so the radius is 1.5 cm. Let's find the area. We will use 3.14 for π.
π×1.5²=7.065
Now, we need to find the area of the walls of the cup. The wall is a rectangle that is basically wrapped around the circle. The height of the rectangle is the height of the cup and the length of the rectangle is the circumference (perimeter) of the bottom circle because the length of the rectangle wraps completely around the circle.
First, let's find the circumference of the circle. The circumference is the diameter (distance across the circle, so 3 cm) multiplied by π. We will use 3.14 for π.
3π=9.42
So, this means that the long side of the rectangle is 9.42 cm, and now we multiply this by the height.
9.42×6.4=60.288
Now, we add the rectangle area and the bottom circle area.
60.288+7.065=67.353
But, they want us to round to the nearest centimetre, so we will just say 67 square centimetres.
An important thing to note is that this is not the area of a normal cylinder (one with a top and a bottom circle) because it is a cup so it does not have a top. If you have a cylinder with a top and a bottom, you would just multiply the area of the circle by two, so then you have the top and bottom. If that were the case, the area of our cylinder would be 74 cm with the numbers we have been given here.
Have a wonderful day!
Which statements about the figure must be true? Select three options. A- Line segment A B is bisected by Line segment C D . B- Line segment C D is bisected by Line segment A B . C- AE = One-halfAB D- EF = One-halfED E- CE + EF = FD
Answer:
C and E
Step-by-step explanation:
Midpoint, as the word suggests, means the point which lies in the middle of something. The statements that are correct are 1, 3, and 5.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
The statements which are correct about the given figure are:
AB is bisected by CD. Since CD bisect the line AB at point E, into two equal parts, therefore, the given statement is true.AE = 1/2 AB. Since CD bisect the line AB at point E, into two equal parts, therefore, the given statement is true.CE + EF = FD. Since F is the midpoint of CD, the length of CF and FD will be equal but also CF is divided into two parts, therefore, AE and Eb.Hence, the statements that are correct are 1, 3, and 5.
Learn more about Midpoint:
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Hera are 4 fractions labelled A,B,C and D 3/4 5/6 16/25 9/15 A B C D Write them in order starting from the smallest
Answer: 9/15, 16/25, 3/4 and 5/6.
Step-by-step explanation:
From the question, we have been given four fractions which are 3/4, 5/6, 16/25 and 9/15. We are told to write them in order starting from the smallest. For this to be done, we will have to change the fractions to percentages. This will be:
3/4 = 3/4 × 100 = 75%
5/6 = 5/6 × 100 = 83.3%
16/25 = 16/25 × 100 = 64%
9/15 = 9/15 × 100 = 60%
From the above percentages, arranging the fractions from the smallest will be:
9/15, 16/25, 3/4 and 5/6.
Good morning
Pls I will like you all to pls put full explanation.
I am preparing for my Exam
Thank you
6/5=3/d
d=?
Answer:
5/2 or 2.5
Step-by-step explanation:
6/5=3/d
6*d=3*5
d=3*5/6
d= 5/2 or 2.5
Answer:
D=2.5Solution,
[tex] \frac{6}{5} = \frac{3}{d} \\ or \: 6 \times d = 5 \times 3(cross \: multiplication) \\ or \: 6d = 15 \\ or \: d = \frac{15}{6} \\ d = 2.5[/tex]
hope this helps...
Good luck..
Please help :(( A candy company has hired you as their new production manager. Your job is to choose the form of packaging for a new product from the five choices below. The candy is animal gummies. The package must hold between 45 and 50 cubic inches (roughly 3 cups of space). The cost of the plastic for the packaging is $0.002 per square inch. Solid 1: Solid 2: Solid 3: Solid 4: Solid 5:
Answer:
sorry please....what is the end of the question ....no task to do
Anyone help me pls,find the area of each figure(All lines meet at right angles.)
Answer:
The Area of the required figure is [tex]315\:cm^2[/tex]
Step-by-step explanation:
[tex]Area = (21\times 7)+(14\times 7) + (7\times 10)\\\\=147+98+70\\\\=315[/tex]
Best Regards!
Suppose babies born in a large hospital have a mean weight of 3366 grams, and a variance of 244,036. 1118 babies are sampled at random from the hospital what is the probability that the mean weight of the sample babies would be greater than 3412 gram answer to four decimal places Round your
Answer: 0.0009
Step-by-step explanation:
Given : Babies born in a large hospital have a mean weight of 3366 grams, and a variance of 244,036.
i.e. [tex]\mu=3366[/tex] and [tex]\sigma^2 = 244036\Rightarrow\ \sigma= \sqrt{244036}=494[/tex]
Sample size = 1118
Let [tex]\overline{X}[/tex] be the sample mean weight of babies.
Then, the probability that the mean weight of the sample babies would be greater than 3412 gram:
[tex]P(\overline{X}>3412)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3412-3366}{\dfrac{494}{\sqrt{1118}}})\\\\=P(Z>\dfrac{46}{14.7743})\ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\\approxP(Z>3.11)\\\\= 1-P(Z<3.11)\\\\=1-0.9991=0.0009[/tex]
Hence, the required probability = 0.0009
If f(x) = x + 8 and g(x) = x3, what is (gºf)(-5)?
Answer:
Step-by-step explanation:
f(-5) = -5 + 8 = 3
g(3) = 3^3 = 27
if x=4 and y=-2, the value of 1/2xy^2 is
a. 32
b. 8
c. -4
d. -8
Answer:
b. 8
Step-by-step explanation:
To solve, we need to plug in the x and y values since we already have the values given to us
1/2(4)(2^2)
We should do the exponents first, 2^2 is 4
Now we are left with 1/2(4)(4)
4 times 4 is 16
16 times 1/2 is the same as 16/2
16/2=8
b. 8