Given:
[tex]\frac{8}{9},\frac{9}{10},\frac{11}{12},\frac{12}{13}[/tex][tex]\frac{8}{9}=0.8889[/tex][tex]\frac{9}{10}=0.9[/tex][tex]\frac{11}{12}=0.9167[/tex][tex]\frac{12}{13}=0.9231[/tex][tex]\frac{8}{9}\text{ is the smallest fraction.}[/tex]katie placed $2500 in a savings account compounded annually at 1.75%. what is the value of her account after 4 years?
We can solve this question using the formula for compound interest:
[tex]F=P\cdot(1+i)^n[/tex]F = ?
P = $2500
i = 1.75
n = 4
Then, we have:
[tex]F=2500\cdot(1+\frac{1.75}{100})^4\Rightarrow F=2679.6475\Rightarrow F=2679.65[/tex]The value of her account after 4 years is about $2679.65.
Find the circumference and area of the circle. Express answers in terms of and then round to the nearest tenth. Part 1. Find the circumference in terms of . C = _ cmPart 2. Find the circumference rounded to the nearest tenth.C = _ cmPart 3. Find the area in terms of A = _ cm2Part 4. Find the area rounded to the nearest tenth. A = _ cm3
Answer:
1. C = 8π cm
2. C = 25.1 cm
3. A = 16π cm²
4. A = 50.3 cm²
Explanation:
Part 1.
The circumference of a circle can be calculated as
[tex]C=2\pi r[/tex]Where r is the radius. So, replacing r = 4 cm, we get:
C = 2π(4 cm)
C = 8π cm
Part 2.
To round the circumference to the nearest tenth, we need to replace π = 3.14, so
C = 8(3.14) cm
C = 25.1 cm
Part 3.
The area of a circle can be calculated as
A = πr²
Replacing r = 4cm, we get:
A = π(4 cm)²
A = 16π cm²
Part 4.
To round to the nearest tenth, we need to replace π = 3.14, so
A = 16(3.14) cm²
A = 50.3 cm²
Therefore, the answers are
1. C = 8π cm
2. C = 25.1 cm
3. A = 16π cm²
4. A = 50.3 cm²
Match the order of the step to the steps to solve this equation2x/3 -6 =2 Column A 1. ___ What is the first step? 2. ___ What is the second step? 3. ___ What is the third step? 4. ___ What is the value of X? Column B a. Multiply both sides by 3 b. Divide both sides by 2 c. X=12 d. Add 6 to both sides Please help me with this.
The first step is to collect like terms:
This is done by adding 6 to both sides of the equation
1) add 6 to both sides (option D)
2x/3 -6+6 = 2+6
2x/3 = 8
The second step is to cross multiply OR
multiply both sides of the equation by 3
2x = 8(3)
2x = 24
2) Multiply both sides by 3 (option A)
The third step is to divide both sides by 2
2x/2 = 24/2
3) Divide both sides by 2 (option B)
x = 24/2
4) x = 12 (option C)
The new strain of covid is spreading at the rate of 12% a week. Currently, there are 100,000 people infected with the virus. How long will it take before the virus has infected 800,000 people?
The covid strain will take 17.33 weeks to infect 800,000 people.
To solve the given problem, we only need to utilize the exponential function formula, which is stated as
[tex]A = Pe^{rt}[/tex]
Where A is the final value,
P denotes the starting value
The rate is r and time is given by t.
Given:
The rate of spread of the new strain of covid = 12% a week
Currently the number of people infected with the virus = 100,000
To determine how long will it take before the virus has infected 800,000 people, substitute the values in the formula
[tex]A = Pe^{rt}[/tex]
[tex]800000 = 100000e^{0.12*t}[/tex]
[tex]8 = e^{0.12*t}[/tex]
[tex]ln 8 = {0.12*t}[/tex]
[tex]t = ln 8/0.12[/tex]
[tex]t = 17.33 weeks[/tex]
Therefore, the covid strain will take 17.33 weeks to infect 800,000 people.
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3. Do these three points create a right triangle?
A(2,2) B(-2-1) C(-3, 2)
Answer:
they do NOT create a right-angled triangle
Step-by-step explanation:
to make a right-angled triangle the side lengths must comply with Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
the side lengths in this ABC triangle are :
AB² = (2 - -2)² + (2 - -1)² = 4² + 3² = 16 + 9 = 25
AB = 5
BC² = (-2 - -3)² + (-1 - 2)² = 1² + (-3)² = 1 + 9 = 10
BC = sqrt(10)
CA² = (-3 - 2)² + (2 - 2)² = (-5)² + 0² = 25
CA = 5
so, this is an isoceles triangle (2 equal legs).
the side lengths 5, 5, sqrt(10) do NOT create a right-angled triangle.
no matter how we combine their squares in the Pythagoras formula, it does not work :
10 = 25 + 25 = 50 no.
25 = 10 + 25 = 35 no.
What is the volume of this triangular Pyramid photo attached
To find the volume of a triangular pyramid, the formula is:
[tex]V=\frac{1}{3}(Area\text{ }of\text{ }thebase)(height)[/tex]So we start by finding the area of the base, which is in the shape of a right triangle in this case.
The area of a right triangle is equal to 1/2 x base x height.
[tex]\begin{gathered} A=\frac{1}{2}bh \\ \\ A=\frac{1}{2}(5)(6) \\ \\ A=15\text{ square feet} \end{gathered}[/tex]We use this area to find the volume.
[tex]\begin{gathered} V=\frac{1}{3}Ah \\ \\ V=\frac{1}{3}(15)(6) \\ \\ V=30\text{ cubic feet} \end{gathered}[/tex]The volume of the triangular pyramid is 30 cubic feet.
Can someone please help with my homework?
NASA launches a rocket at t=0 seconds. Its height, in meters above sea level, as a function of time is given by h(t) = −4.9t^2 + 241t + 402 Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
1. The rocket splashes down after________seconds.
2. How high above sea level does the rocket get at its peak? The rocket peaks at_________ meters above sea level.
Considering the given quadratic function, it is found that:
1. The rocket splashes down after 50.8 seconds.
2. The rocket peaks at 3365.3 meters above sea level.
When does the rocket splashes down?The height of the rocket after t seconds is given according to the following rule:
h(t) = -4.9t² + 241t + 402.
Which is a quadratic equation with coefficients given by:
a = -4.9, b = 241, c = 402.
It splashes down when it hits the ground, that is, when h(t) = 0, hence:
-4.9t² + 241t + 402 = 0.
Then:
[tex]\Delta = 241^2 - 4(-4.9)(402) = 65960.2[/tex][tex]x_1 = \frac{-241 + \sqrt{65960.2}}{-9.8} = -1.62[/tex][tex]x_2 = \frac{-241 - \sqrt{65960.2}}{-9.8} = 50.8[/tex]Time is a positive measure, hence it splashes down after 50.8 seconds.
What is the maximum height?The height of the rocket is a concave down quadratic equation, hence the maximum height is the y-coordinate of the vertex, given as follows:
[tex]h_{MAX} = -\frac{\Delta}{4a}[/tex]
Both these parameters have been found in the previous item, hence:
[tex]h_{MAX} = -\frac{65960.2}{4(-4.9)} = 3365.3[/tex]
3365.3 meters.
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|4x - 5| = 8A. x= 13/4 or x= -3/4B. x= 3/4 or x= -13/4C. x= 13/4 onlyD. no solutionE. infinitely many solutions
We will solve this problem thus:
[tex]\begin{gathered} \lvert4x-5\rvert=8 \\ \text{means} \\ 4x-5=+8\text{ or 4x-5= -8} \end{gathered}[/tex]Solving further we will have:
[tex]\begin{gathered} 4x=8+5\text{ or 4x=-8}+5 \\ 4x=13\text{ or 4x = -3} \\ x=\frac{13}{4}\text{ or x=}\frac{-3}{4} \\ \text{The correct answer is option A} \end{gathered}[/tex]Though 70% of women with children younger than 18 years participate in the labor force, society still upholds the stay-at-home mother as the traditional model. Some believe that employment distracts mothers from their parenting role, affecting the well-being of children. In the GSS 2014, respondents were asked to indicate their level of agreement to the statement, “A working mother hurts children.” Of the 435 male respondents who answered the question, 18% strongly agreed that a working mother does not hurt children.
Using the z-distribution, the 95% confidence interval for the proportion of male respondents that agree that a working mother does not hurt children is:
(0.1439, 0.2161).
What is a confidence interval of proportions?The bounds of a confidence interval of proportions is given according to the following rule:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the parameters are described as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The values of the other parameters are given as follows:
[tex]\pi = 0.18, n = 435[/tex]
Hence the lower end of the interval is calculated as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 - 1.96\sqrt{\frac{0.18(0.82)}{435}} = 0.1439[/tex]
The upper end of the interval is calculated as follows:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 + 1.96\sqrt{\frac{0.18(0.82)}{435}} = 0.2161[/tex]
Missing informationThe problem asks for the 95% confidence interval for the proportion of male respondents that agree that a working mother does not hurt children is:
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Determine whether each sample method is unbiased or biased. If the method is unbiased, use it to make a prediction. If the method is biased, explain why. 1. A cable company representative randomly calls 250 households to determine how many customers subscribe to the movie channels. Of the 250 households contacted, 22% do not subscribe to movie channels. If there are 5,240 customers, how many do not subscribe to movie channels.
The representative took a sample to estimate the proportion of customers that do not subscribe to movie channels.
He took a sample from the customer base and the sample proportion he gets is 22% (p = 0.22). This sample proportion is an unbiased estimator of the populations proportion, so we can use it to calculate how many customers do not subscribe to movie channels:
[tex]n=N\cdot p=5240\cdot0.22\approx1153[/tex]Answer: we can estimate that there are 1153 customers that do not subscribe to movie channels.
Statically question
Answer: We have to select the statistical questions out of the given options,
the statistical questions are any questions that involve the use of data, therefore following options are the statistical questions:
[tex]\begin{gathered} \text{ Following Options:} \\ \\ (1)\text{ \lparen2\rparen and }(4) \end{gathered}[/tex]Therefore (1) (2) and (4) use the data, they are the statistical questions.
the sum of -5 and six times a number
Six times menas multiply by six:
a number = x
The sum of -5 and six times a number
-5 + 6x
4
A TV that usually sells for $167.77 is on sale for 15% off. If sales tax on the TV is 6%, what is the price of the TV, including tax?
OA. $201.49
OB. $152.59
OC. $151.16
OD.
$149.73
The price including tax is $151.16
What is tax?
A tax is a mandatory financial charge or other type of levy imposed by a governmental organization on a taxpayer (an individual or legal entity) in order to fund government spending and various public expenditures (regional, local, or national), and tax compliance refers to policy actions and individual behavior aimed at ensuring that taxpayers pay the correct amount of tax at the correct time and receive the correct tax allowances and tax reliefs. The earliest known taxes occurred in Ancient Egypt between 3000 and 2800 BC. Failure to pay on time (non-compliance), as well as avoidance or resistance to taxation, is illegal and punished by law. Taxes can be paid in cash or in labor equivalents and can be direct or indirect.
Selling price of TV = $167.77x0.85 (15% discount)
= $142.6025
Price of TV (including tax) = $142.6025x1.06 (6% tax)
= $151.16
Hence, the price including tax is option (c) $151.16
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If a running back runs 28 yards in the first quarter, how many yards can you expect him to gain
throughout the game?
Answer:
112 yards
Step-by-step explanation:
quarter is 1/4 right¿
28 × 4 = 112
Match the area formula with the correct polygon. A = 1/2bh parallelogram A = bh triangle A = 1/2 (b1 + b ) + trapezoid
The area of a parallelogram can be determined by multiplying its base and height, the formula is
[tex]A=bh[/tex]The area of a triangle is equal to half the product between the base and the height, following the formula:
[tex]A=\frac{1}{2}(bh)[/tex]The area of a trapezoid is equal to the product of half the sum of its bases and its height following the formula:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]Abdul drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Abdul drove home, there was no traffic and the trip only took 6 hours. If his average rate was 16 miles per hour faster on the trip home, how far away does Abdul live from the mountains? Please show work because it doesn’t make sense any other way!
solve for x using the figure below. (view image)
The value of x in the figure is 3
How to find x from the figure?
Let us re -write the given values as fractions
[tex]\frac{5}{8} =\frac{x+3.25}{10} \\\\[/tex]
By applying cross multiplication method,
5(10) = 8(x+3.25)
50 =8x +26
8x = 50-26
8x = 24
x = 3
Similarly re- writing next set of vales as fractions,
[tex]\frac{2}{5} =\frac{2.5}{x+3.25} \\\\[/tex]
By applying cross multiplication method,
2(x+3.25) = 5(2.5)
2x+6.5 = 12.5
2x = 12.5 - 6.5
2x = 6
x = 3
What is cross multiplication of fractions?
To cross multiply two fractions, multiply the denominator of one by the numerator of the other, and then compare the results. The larger fraction is the one having the larger value.Virtually all fractions that are cross multiplied will have various denominators. It is a quick way to compare fractions by reducing them to a common denominator.To learn more about cross multiplying fractions, refer:
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Elon has removed two dead batteries from a flashlight and inadvertently mingled them with the two good batteries he intended as replacements. The four batteries look identical. Elon now randomly selects two of the four batteries. What is the probability he selects the two good batteries? (Hint: sampling is without replacement here)
The probability of the required event is [tex]\frac{1}{2}[/tex]
Number of batteries removed by Elon = 2
And then he mixed these batteries with the other two batteries
Thus total number of batteries = 4
These 4 batteries as given is identical
Now since it is given in the question that there aren't any replacements thus it means that we don't have to apply the Baye's theorem. So we can simply write it as it is mentioned below.
Thus the probability of taking out two batteries which are good without any replacement :
Probability = [tex]\frac{number of outcomes }{total number of favorable outcomes}[/tex]
Given number of outcomes = 2
Total number of favorable outcomes = 4
Thus the probability of the given event is = [tex]\frac{2}{4}[/tex]
Thus P( E ) = [tex]\frac{1}{2}[/tex]
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The common factors of 36, 240, and 504
Answer: 1, 2, 3, 4,6 12
Step-by-step explanation:
every single number can be divided by the answer numbes
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative. This eliminates all of the options except for d.
Find the missing angle:
?=
134⁰
Answer: 46
Step-by-step explanation:
180 - 134 = 46
Help, please, it's urgent
∠10 and ∠16 are Alternate exterior angles, ∠4 and ∠12 are Consecutive exterior angles, ∠12 and ∠13 are Consecutive Interior angles and ∠3 and ∠9 are Alternate Interior angles.
1. If two lines which are in the same plane are intersected by another line at two different lines, eight angles are formed, and that another line is called the transversal.
In the provided figure,
In the angles,
∠10 and ∠16, q is the transversal and these are Alternate exterior angles.
∠4 and ∠12, n is the transversal and these are Consecutive exterior angles.
∠12 and ∠13, q is the transversal and these are Consecutive Interior angles.
∠3 and ∠9, n is the transversal and these are Alternate Interior angles.
2. Referring tot the cube ABCDHGFE,
a. All planes that are parallel to the plane DEH are CBF and FGC.
b. All segments that are parallel to AB are EF, HG and DC.
c. All segments that intersect GH are EH, HG, FG and CG.
d. All segments that are skew to CD are AB, EF and HG.
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Really need help solving thisIt’s trigonometry It’s from my ACT prep guide
We have the following configuration for this problem:
where y is the distance, in feet, Corey stepped back.
Then, we have:
[tex]\begin{gathered} \tan 68\degree=\frac{80}{x} \\ \\ x=\frac{80}{\tan 68\degree} \end{gathered}[/tex]And:
[tex]\begin{gathered} \tan 41\degree=\frac{80}{x+y} \\ \\ x+y=\frac{80}{\tan 41\degree} \\ \\ y=\frac{80}{\tan 41\degree}-x \end{gathered}[/tex]Now, using the first into the second equation, we obtain:
[tex]\begin{gathered} y=\frac{80}{\tan41\degree}-\frac{80}{\tan 68\degree} \\ \\ y=59.71 \end{gathered}[/tex]Therefore, Corey stepped back approximately 59.71 feet.
[tex] \frac{5}{3}s = \frac{15}{3} + \frac{3}{2}s - \frac{1}{4} [/tex]i dont under stand it and other questions like it because I'm sorta slower than the rest of my class. We're doing Types of Solutions of Linear Equations.
The question we have to solve is:
[tex]\frac{5}{3}s=\frac{15}{3}+\frac{3}{2}s-\frac{1}{4}[/tex]To solve this equation, we take all the "s"'s to one side and numbers to the other and simplify:
[tex]\begin{gathered} \frac{5}{3}s=\frac{15}{3}+\frac{3}{2}s-\frac{1}{4} \\ \frac{5}{3}s-\frac{3}{2}s=\frac{15}{3}-\frac{1}{4} \\ \frac{5(2)-3(3)}{6}s=\frac{15(4)-1(3)}{12} \\ \frac{1}{6}s=\frac{57}{12} \\ s=\frac{\frac{57}{12}}{\frac{1}{6}} \end{gathered}[/tex]When we want to divide by a fraction, we mulitply by its reciprocal. So,
[tex]\begin{gathered} s=\frac{\frac{57}{12}}{\frac{1}{6}} \\ s=\frac{57}{12}\times\frac{6}{1} \\ s=\frac{57}{2} \end{gathered}[/tex]pls help 9th grade geometry
Answer:
< 6 = 58°
< 8 = 58°
< 5 = 122°
<7 = 122°
Step-by-step explanation:
<6 = <8 because corresponding angles are equal
5y + 13 = 7y -5 Subtract 5 y from both sides
13 = 2y -5 Add 5 to both sides
18 = 2y
9 = y
Now that we know that y = 9, we plug it back into either equation
5y + 13
5(9) + 13
45 + 13
58
<5 is supplemental to <6 so 180 - 58 = 122
<8 is supplemental to < 7 so it is 122 also
Find X.
Circumscribed Angles
Answer:
x=20
Step-by-step explanation:
To find x you must first set up an equation. (3x+90+90+120=360) the reason why i did that is because the red boxes indicate that they are 90° angles. They add up to 360 is because the quadrilaterals add up to 360. after solving for x, you should get x = 20.
A tree trunk may be considered a circular cylinder.
Suppose the diameter of the trunk increases 1 inch per
year and the height of the trunk increases 6 inches per
year. How fast is the volume of wood in the trunk
increasing when it is 100 inches high and 5 inches in
diameter?
The volume of the tree trunk increases 52.64% in one year.
Given,
The height of a tree trunk = 100 inches
The diameter of a tree trunk = 5 inches
Diameter increases 1 inch per year
Height increases 6 inches per year
We have to find the increase in its volume.
Consider the trunk as a circular cylinder.
Volume of circular cylinder = πr²h
Radius, r = 5/2
Height, h = 100
Initial Volume = πr²h
Volume = π × (5/2)² × 100 = π × 6.25 × 100 = 1963.50 cubic inches
After one year
Diameter = 6
Height = 106
Increased Volume = πr²h
Volume = π × (6/2)² × 100 = π × 9 × 106 = 2997.08 cubic inches
The rate of increase in volume = (Increased volume × 100) ÷ Initial volume
= (2997.08 × 100) ÷ 1963.50 = 152.64
That is,
The volume of the tree trunk increases 52.64% in one year.
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5. Among 100 students, 60 participated on playing games and 50 participated in music. How many students participated in both the activities? Also find how many students participated in music only?
In 4 1/2 hours Greg reads 9 3/4 chapters what is the unit rate in chapters per hour
2 1/6 is the answer
9 3/4 divided by 4 1/2 = 2 1/6
Write the numbers in increasing order with a comma separating eachnumber: 1.99, -3.45, 2.01, -3.42, 0.99
To write the numbers in increasing order, we start from the most negative to the most positive:
[tex]-3.45,-3.42,0.99,1.99,2.01.[/tex]Answer
-3.45, -3.42, 0.99, 1.99, 2.01