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
Two circles have radii of 4 units and 6 units. What is the radius of a circle whose area is equal to the sum of the areas of the two given circles?
Answer:
Step-by-step explanation:
We that the area of a circle is Pi times r^2 where r is the radius
Let A be the area of the first circle and S the area of the second one and T the total one
A=4^2× Pi
S=6^2× Pi
T = Pi( 4^2 +6^2)
= Pi ( 16+36) = Pi× 52
52 is the radius square
So r = root square 52 = 2 root square 13
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
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
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
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).
Find the simple interest on a loan of 20,000 at the rate of 5% in 3 years
Answer:
3,000
Step-by-step explanation:
Loan = 20,000
Simple Interest per year = 5% of 20,000
=> [tex]\frac{5}{100}* 20,000[/tex]
=> 5 * 200
=> 1,000
Simple Interest for 3 years = 3 * 1000
=> 3,000
Answer:
3000
Step-by-step explanation:
SI = P × R × T
Use simple interest formula.
20000 × 5% × 3
1000 × 3
= 3000
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.
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!
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.
Consider this complex fraction. Which division problem is represented in the picture? Two-thirds divided by 3 and one-third 3 and one-third divided by (three-halves) 3 (two-thirds) 3 and one-third divided by 5
Answer:
This represents 3 and one-third divided by two-thirds because 10/3 = 3 and 1/3.
Answer:
It is 3 and 1/3 divided by 2/3. None of the choices given work.
Hope it helps <3
Are rectangles ABCD and WXYZ congruent? Why or why not? Yes, all right angles were preserved. Yes, both rectangles have an area of 24 square units. Yes, a 180° rotation about the origin will map ABCD to WXYZ. No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.
Answer:
D. No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.
Step-by-step explanation:
Two figures are congruent if their vertices can be mapped into one another by appropriate rigid transformation or combination of rigid transformations. Examples of the transformation are; reflection, dilation, rotation and translation.
Comparing the two figures, it would be observed that they are not congruent. Since there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.
Answer:
it is D just took the test
Step-by-step explanation:
Which of the following compositions of transformations will always produce the same image, regardless of the order in which the transformations are performed?
Answer:
All compositions are affected by the order in which they are performed
Step-by-step explanation:
We have the following transformations:
-translation
-reflection
-rotation
Each of them are affected by the order in which they are performed, for example:
If we rotate we have:
(x, y) -> (y, -x).
After the reflection:
(y, -x) -> (-y, -x).
If we translated by <2, 5> and reflected through the y-axis:
After the translation, (x, y) -> (x + 2, y + 5)
In other words, all compositions are affected by the order in which they are performed
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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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
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
Examine the diagram, and answer the question. The points A(2,7) and B(−4,−3) are located in the coordinate plane as shown. Points A and B are shown in the coordinate plane at the locations indicated. What is the approximate distance between the two points?
Answer:
Option (2)
Step-by-step explanation:
Formula to get the distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
The given points are A(2, 7) and B(-4, -3)
Distance between these points will be,
AB = [tex]\sqrt{(2+4)^2+(7+3)^2[/tex]
= [tex]\sqrt{6^2+10^2}[/tex]
= [tex]\sqrt{136}[/tex]
= 11.66
≈ 11.7 units
Therefore, distance between the points A and B is 11.7 units.
Option (2) will be the answer.
Answer:
For those with the square root answer its 2\sqrt(34)
Step-by-step explanation:
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
a fruit drink is made by mixing 60ml of orange juice with 180ml of pineapple juice. what is the ratio of orange juice to pineapple juice in its simplest form?
Answer:
1:3
Step-by-step explanation:
both divide by 60 so do 60 divided by 60 which is one
then 180 divided by 60 which is three
this gives you the answer
Answer:
1:3
Step-by-step explanation:
a ratio is basically the same as a fraction just in a different form. so it would be 60/180 simplified. both 60 and 180 can be divided by 60. so you would divide both numbers by 60 to get 1/3. this cannot be simplified any further. then to put it as a ratio it would just be 1:3
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
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].
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]
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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
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:
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..
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.
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.
Which graph has figures that can undergo a similarity transformation to justify that they are similar?
ty
Answer:
it is the second option
Step-by-step explanation:
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:
Pick all that apply the option answer in two minutes
Answer: PQT and TUV
Step-by-step explanation: