Answer:
134217728
Step-by-step explanation:
The geometric sequence formula is:
[tex]\displaystyle{a_n = a_1r^{n-1}}[/tex]
We know that [tex]\displaystyle{a_1=8}[/tex] and [tex]\displaystyle{r=2}[/tex], we also want to find the 25th term, substitute n = 25:
[tex]\displaystyle{a_{25}=8\cdot 2^{25-1}}\\\\\displaystyle{a_{25}=8\cdot 2^{24}}\\\\\displaystyle{a_{25}=134217728}[/tex]
Therefore, the 25th term of sequence is 134217728
The table below gives recommended weight ranges for the balls from five different sports. (Hint: Find the average of each weight.)
The average weights of each ball are 270 grams, 625 grams, 425 grams, 145.5 grams and 14.5 ounces
How to determine the average weights?The range is given as:
Sport Weight range of ball used
Volleyball 260-280 grams
Basketball 600-650 grams
Water Polo 400-450 grams
Lacrosse 142-149 grams
Football 14-15 ounces
The average of each weight is calculated as:
Average = (Max + Min)/2
So, we have:
Volleyball = (260+280)/2 = 270 grams
Basketball = (600+ 650)/2 = 625 grams
Water Polo = (400+450)/2 = 425 grams
Lacrosse = (142+149)/2 = 145.5 grams
Football = (14+15)/2 = 14.5 ounces
Hence, the average weights of each ball are 270 grams, 625 grams, 425 grams, 145.5 grams and 14.5 ounces
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Missing information in the question
Sport Weight range of ball used
Volleyball 260-280 grams
Basketball 600-650 grams
Water Polo 400-450 grams
Lacrosse 142-149 grams
Football 14-15 ounces
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is
summarized in the histogram below.
What is the sample size for this data set?
Explanation:
Add up the heights of each bar to get the sample size.
4+4+7+12+11+4+1 = 43
Which of the following is equal to the rational expressions when x=2or1? (X-1)/(x+5)/(x-2)/(x-1)
Answer:
(x-2)/(x-1)
Step-by-step explanation:
(x-2)/(x-1)
find x and y.
someone pls help !
Hello !
3y + 12 =2(y + 30)
⇔ 3y + 12 = 2y + 60
⇔ y + 12 = 60
⇔ y = 60 - 12
⇔ y = 48
Answer:
y = 48
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
3y + 12 is an exterior angle of the triangle , so
3y + 12 = y + 30 + y + 30 ( base angles of an isosceles Δ are congruent )
3y + 12 = 2y + 60 ( subtract 2y from both sides )
y + 12 = 60 ( subtract 12 from both sides )
y = 48
The following present value factors are provided for use in this problem.
Periods Present Value
of $1 at 8% Present Value of an
Annuity of $1 at 8%
1 0.9259 0.9259
2 0.8573 1.7833
3 0.7938 2.5771
4 0.7350 3.3121
Xavier Co. wants to purchase a machine for $37,500 with a four year life and a $1200 salvage value. Xavier requires an 8% return on investment. The expected year-end net cash flows are $12,500 in each of the four years. What is the machine's net present value?
$(3901).
$3901.
$4783.
$(4783).
$42,283.
The net present value of machine is $5982
What is investment?An investment is an asset or item acquired with the goal of generating income or appreciation.
As, 4th Year Cash Flow
= Salvage Value + Expected End Year Net Cash Flow
= $1,200 + $12,500
= $13,700
Year Cash flow ($) PVF at 8% Present value ($)
0 37,500 1.000 -36,300
1 12,500 0.9259 11573.75
2 12,500 0.8573 10716.25
3 12,500 0.7938 9922.5
4 13,700 0.7350 10069.5
Net value 5982
Hence, net present value of machine is $5982
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Solve the logarithmic equation...
Answer:
x = 3
Explanation:
[tex]\sf Given \ equation: \ log_{10} (1000) = x[/tex]
Solving steps:
[tex]\rightarrow \sf log_{10} (1000) = x[/tex]
apply rule: logₐ(b) = c then b = aᶜ
[tex]\rightarrow \sf 1000 = 10^x[/tex]
rewrite following
[tex]\rightarrow \sf 10^3= 10^x[/tex]
cancel out bases
[tex]\rightarrow \sf x = 3[/tex]
Answer:
d.) x = 3
Step-by-step explanation:
you simply need to know 10 to power of how many makes 1000 , In case didn't know you can replace the value of x with the given options and see if it can be solved or not .
The function g(x) = p sin x +q, where p>0, has a maximum value of 10 and a minimum value of -4. Find the value of p and of q.
Answer: [tex]p=7, q=3[/tex]
Step-by-step explanation:
The midline of the function is
[tex]\frac{10-4}{2}=3 \implies q=3[/tex]
This means that to obtain a maximum of 10, when [tex]\sin x[/tex] reaches it's maximum, 1, [tex]g(x)=p+q=10 \implies p=7[/tex]
A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be __________.
A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be 0 to -1. Then the correct option is A.
What is a correlation coefficient?A mathematical indicator of the degree of the association seen between fluctuation of 2 factors is the correlation coefficient.
A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be 0 to -1.
Then the correct option is A.
The complete question is attached below.
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Which amount of time is greater for the average person? The total time spent on his/her cell phone in a year’s time, or the total time spent waiting in line when shopping in a lifetime?
Consider it to be 2 separate problems and arrive at your conclusion.
You need to make assumptions, conversions, and math calculations to arrive at your answer. If you choose to research data for this project, that is fine but there is no need to site your references.
The total time spent on his/her cell phone in a year’s time is less than the total time spent waiting in line when shopping in a lifetime.
x= 1825 hrs
z=4929.4 hrs.
This is further explained below.
Which amount of time is greater for the average person?let's say on average a person spends 5 hours on a mobile phone.
Individual annual mobile phone use time.
x= 5x365
x= 1825 hrs
let's consider an average every day a person, spent 5 minutes in the queue when shopping.
Take the average person. 70-year life for a person.
Hence in a year, he spent
y=365x5 mints
y=1825 min
y=30.42 hrs
Hence lifetime time spent on line
z = 70 x 30.42
z=4929.4 hrs.
In conclusion, we estimate that the typical individual will spend z=4929.4 hours waiting in line for merchandise throughout the course of their lifetime.
z=4929.4 hrs.
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2.3. Use the following subtraction strategies to calculate 884-597: 2.3.1. breaking up the second number 2.3.2. adding on to the smaller number until you reach the bigger number 2.4. Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition. (4) (3) (3) 2.5. Suppose you want to have the activity in 2.4 marked by peers. Give a marking guideline according to which learners can score each other's work. (2) 2.6. Draw a diagram by which you can visually explain to learners in the Intermediate Phase why the sum of five consecutive numbers is equal to the fifth multiple of the middle number. Choose any set of five consecutive numbers to illustrate your statement. Write down your explanation in four powerful sentences. (5) OW a 2.3 . Use the following subtraction strategies to calculate 884-597 : 2.3.1 . breaking up the second number 2.3.2 . adding on to the smaller number until you reach the bigger number 2.4 . Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition . ( 4 ) ( 3 ) ( 3 ) 2.5 . Suppose you want to have the activity in 2.4 marked by peers . Give a marking guideline according to which learners can score each other's work . ( 2 ) 2.6 . Draw a diagram by which you can visually explain to learners in the Intermediate Phase why the sum of five consecutive numbers is equal to the fifth multiple of the middle number . Choose any set of five consecutive numbers to illustrate your statement . Write down your explanation in four powerful sentences . ( 5 ) OW a
It should be noted that the value of 597 subtracted from 884 is 287.
How to illustrate the subtraction?The information is simply that we should subtract 884 and 597 and also illustrate it.
This will be:
884 - 597 = 287.
A word problem illustrating this is that a man had 884 pens and gave 597 pens to his friends. How many pens does he have left?
This will be:
= 884 - 597 = 287
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Determine if
16
x
2
−
25
y
2
=
1
16
x
2
-
25
y
2
=
1
is a hyperbola and if it is, which type it is. The transverse axis is
what is A and B
The values of a and b are 1/4 and 1/5 respectively
How to determine the true statement?The function is given as:
16x^2 - 25y^2 = 1
The above function is a horizontal hyperbola.
A horizontal hyperbola that passes through the origin is represented as:
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
Rewrite 16x^2 - 25y^2 = 1 as
[tex]\frac{x^2}{1/16} - \frac{y^2}{1/25} = 1[/tex]
By comparison, we have:
[tex]a^2 = \frac{1}{16}[/tex]
[tex]b^2 = \frac{1}{25}[/tex]
Solve for a and b
[tex]a = \frac{1}{4}[/tex]
[tex]b = \frac{1}{5}[/tex]
Hence, the values of a and b are 1/4 and 1/5 respectively
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QUESTION IS DOWN BELOW 30 points for answer
Answer: a) 25:16 and b) 125:64
Step-by-step explanation:
For simplicity, assume that two spheres have diameters of 5 and 4.
a) 4pi(5^2) and 4pi(4^2)
= 100pi:64pi
= 100:64
= 25:16
b. 4/3 pi(5^3) and 4/3 pi(4^3)
= 166.67pi and 85.33pi
= 500:256
= 125:64
A shape is picked at random from this group. Which theoretical probabilities are exactly 3/4?
Check all that apply.
not picking a triangle
picking a square
picking a shape with only straight edges
not picking a circle
not picking a square
Probability helps us to know the chances of an event occurring. The correct option is D, not picking a circle.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
For the theoretical probability to be 3/4, the number of desired outcomes must be 6. Therefore, let's check the number of desired outcomes,
Not picking a triangle = 4
Picking a square = 3
Picking a shape with only straight edges = 0
Not picking a circle = 6
Not picking a square = 5
Hence, the correct option is D, not picking a circle.
The group of the shape is given in the below image.
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what’s the answer to 3\4(8x + 12) = 3
Answer:
x = - 1
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] (8x + 12) = 3 ( multiply both sides by 4 to clear the fraction )
3(8x + 12) = 12 ( divide both sides by 3 )
8x + 12 = 4 ( subtract 12 from both sides )
8x = - 8 ( divide both sides by 8 )
x = - 1
You are volunteering to help with the soccer team fundraiser for Valentine's Day. Your team promised to deliver one 16 ounce bag of nuts to students with at least 60% chocolate-covered nuts inside.
When you arrive, instead of a bag of plain nuts and chocolate nuts, you find there are two bags of mixed nuts. The first says it is 50/50 plain and chocolate covered. The second bag contains 80% chocolate covered nuts.
The team is dismayed, but you come up with a solution. You suggest combining
ounces* of the 50/50 bag of nuts with
ounces* of the 80% bag of nuts, to make it an approximately 60% mixture.
*estimate
Then another student on the team says, "Wait, we promised at least 60%. So if we just do half and half won't we be giving them at least 60%?" This student
correct.
The student, who suggests that if we do half and half of each bag, we will be giving them at least 60%, is correct.
What is the implication of the phrase "at least"?The phrase "at least" means the minimum that is true or possible.
Mathematically, by "at least," we mean 'equal to or greater than.'
Data and Calculations:Since each bag of nuts contain 16 ounces,
The 1st bag contains x/2 ounces (50%) of plain nuts and x/2 ounces (50%) of chocolate-covered nuts.
The 2nd bag contains x/5 ounces (20%)of plain nuts and 4x/5 ounces (80%) of chocolate-covered nuts.
If half of the 1st bag is mixed with half of the 2nd bag, each bag will contain only 65% (that is, 25% (50%/2) from the 1st bag and 40% (80%/2) from the 2nd bag).
Thus, the student, who suggests that if we do half and half of each bag, we will be giving them at least 60%, is correct since they will not be given less than 60% of chocolate-covered nuts inside.
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PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
Which of the following could be solution to the equation below?
[tex]cos(3x+4)=sin(2x+6)[/tex]
A. x = 2, sin 10° = cos 10°
B. x = 16, sin 52° = cos 38°
C. x = 34, sin 74° = cos 106°
D. x = 16, sin 38° = cos 52°
Using complementary angles, it is found that a solution to the given equation is:
D. x = 16, sin 38° = cos 52°.
What are complementary angles?
Two angles are called complementary if the sum of their measures is of 90º. If two angles A and B are complementary, we have that:
cos(A) = sin(B) and sin(A) = cos(B).
In this problem, the expression is:
cos(3x + 4) = sin(2x + 6).
Hence:
3x + 4 + 2x + 6 = 90
5x = 80
x = 16.
Then:
cos(3x + 4) = cos(52).sin(2x + 6) = sin(38).Which means that option D is correct.
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These 3 points are on a parabola defining the edge of a ski:
(-4,1)
(-2,0.94)
(0,1)
The general form for the equation of a parabola is .
1.
Use the x- and y-values of 1 to build a linear equation with 3 variables: A, B, and C.
Repeat this process with the other 2 points to build a 2nd linear equation.
Record all three equations in the box below.
2.
Build a matrix equation that represents this system of equations. Record your matrix equation here.
3.
Use a graphing calculator or other graphing utility to find the inverse of the coefficient matrix. Record your result here.
4.
Use the inverse matrix to solve the system of equations. Record the equation of the parabola here.
The equation of the parabola is y = 0.015x^2 + 0.06x + 1
The linear equationsA parabola is represented as:
y = ax^2 + bx + c
The points are given as:
(-4,1), (-2,0.94) and (0,1)
When these points are substituted in y = ax^2 + bx + c, we have the following linear equations
16a - 4b + c = 1
4a - 2b + c = 0.94
c = 1
The matrix that represent the system of equationsIn (a), we have:
16a - 4b + c = 1
4a - 2b + c = 0.94
c = 1
Remove the variables (leaving the coefficients)
a b c
16 -4 1 1
4 -2 1 0.94
0 0 1 1
So, the matrix representation of the system of equations is:
[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right] \left[\begin{array}{c}1&0.94&1\end{array}\right][/tex]
The inverse of the coefficient matrixUsing a graphing calculator, we have the inverse of the coefficient matrix to be
[tex]\left[\begin{array}{ccc}0.125&-0.25&0.125\\0.25&-1&0.75\\0&0&1\end{array}\right][/tex]
The solution to the system of equationsUsing a graphing calculator, we have the solution to the system of equations to be
a = 0.015
b = 0.06
c = 1
Recall that:
y = ax^2 + bx + c
So, we have:
y = 0.015x^2 + 0.06x + 1
Hence, the equation of the parabola is y = 0.015x^2 + 0.06x + 1
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In the coin flipping lab, suppose that you simulated the flipping of a weighted coin 30 times and got 5 heads and 25 tails. What is your estimated probability for P(H)?
Answer:
1/6
Step-by-step explanation:
Out of 30 tosses, 5 come up heads. So the estimated probability of heads is 5/30, or 1/6.
Answer: 0.17
Step-by-step explanation:
just got it right on quiz
PLEEEEEEEEEEASSEEEEEEE ANSWER QUESTION IS DOWN BELOW WORTH 15 POINTS each
A ratio shows us the number of times a number contains another number. The ratio of the volume of the model to the volume of the original is 27/2744.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that the scale factor is 3:14. Therefore, the ratios can be written as,
(a) The ratio of the surface area of the model to the surface area of the original is,
Surface area Ratio = (3/14)² = 9/196
(b) The ratio of the volume of the model to the volume of the original.
Volume Ratio = (3/14)³ = 27/2744
(c) The ratio of the width of the model to the width of the original.
Width Ratio = 3/14
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On a number line 1.77 would be located.
On a number line 1.77 would be located between 1 and 2 but it would be closer to 2 than 1.
Where would 1.77 be located?A number line is used to show the positioning of numbers. 1.77 is between 1 and 2. So, it would be located between 1 and 2 on the number line. Because 1.77 can be rounded off to 2, it would be closer to 2.
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In a relatively pointless survey, the following data was collected on cars in a Costco parking lot: there were 94 white cars; 44 purple cars; 41 dark gray cars; 27 light blue cars; 46 green cars; 19 cars of some other color.
If you were to construct a Pareto chart (using the rule suggested in the book), how would the second bar in the graph be labeled?
color =
If I am to to construct a Pareto chart based on the rule of the chart, the second bar color in the graph be labeled light blue.
What is a Pareto chart?A Pareto chart is known to be a form of a bar graph.
It is made up of different lengths of bars that stands for frequency or cost ( e.g. time or money, and are said to be placed with longest bars on the left and then the shortest are placed to the right.
Since there are 27 light blue cars and this is the first one among the shortest, one can make it to be in the second bar and as such, If I am to to construct a Pareto chart based on the rule of the chart, the second bar color in the graph be labeled light blue.
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In a random sample of 1214 eligible voters younger than 40 years old, 461 reported that they planned to vote in the upcoming election. In a random sample of 1098 voters 40 and older,560 reported that they planned to vote in the election. Construct a 90% confidence interval for the difference between the percent of all voters younger than 40 and 40 and older who plan to vote in the upcoming election. What critical z-score will be used
Using the z-distribution, with a critical z-score of z = 1.645, the 90% confidence interval is (-16.4%, -9.66%).
What are the mean and the standard error for the distribution of the difference of proportions?For each sample, the mean and the standard error are given as follows:
[tex]p_y = \frac{461}{1214} = 0.3797, s_y = \sqrt{\frac{0.3797(0.6203)}{1214}} = 0.0139[/tex].[tex]p_o = \frac{560}{1098} = 0.51, s_o = \sqrt{\frac{0.51(0.49)}{1098}} = 0.0151[/tex].Hence, for the distribution of differences, they are given as follows:
[tex]p = p_y - p_0 = 0.3797 - 0.51 = -0.1303[/tex].[tex]s = \sqrt{s_y^2 + s_o^2} = \sqrt{0.0139^2 + 0.0151^2} = 0.0205[/tex]What is the confidence interval?
The interval is:
[tex]p \pm zs[/tex]
In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
Then the bounds of the interval are:
p - zs = -0.1303 - 1.645(0.0205) = -0.164.p + zs = -0.1303 + 1.645(0.0205) = -0.0966.As a percentage, the 90% confidence interval is (-16.4%, -9.66%).
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HELP ASAP!!!!GIVING BRAINLIEST!!!!!!
If f(x)=2x^2+2 and g(x)=x^2-1, find (f-g)(x).
Answer: B. x^2 + 3
Step-by-step explanation:
2x^2 + 2 -(x^2 - 1)
2x^2 + 2 - x^2 + 1
x^2 + 3
Which expression is equivalent to the following complex fraction?
-2/x + 5/y / 3/y - 2/x
Answer: [tex]\frac{5x-2y}{3x-2y}[/tex]
Step-by-step explanation:
[tex]\frac{-\frac{2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}[/tex]
Multiplying the numerator and denominator by xy,
[tex]=\frac{-2y+5x}{3x-2y}\\\\=\frac{5x-2y}{3x-2y}[/tex]
Compare A and B in three ways, where A = 1.8 million is the 2012 population of city X and B = 2.6 million is the 2012 population of city Y.
a. Find the ratio of A to B.
b. Find the ratio of B to A.
c. Complete the sentence: A is ____ percent of B.
Given: Triangle ABC, mmBC=24 cm, line segment AL- < bisector
Find: AL
AL= __cm
Please answer in detail ASAP thank you so much it would help a lot <3
The value of line AL is 21. 51cm
How to determine the lengthTo find line AL,
Using
Sin α = opposite/ hypotenuse to find line AB
Sin 90 = x/ 24
1 = x/24
Cross multiply
x = 24cm
Now, let's find line AC
Sin angle B = line AC/24
Note that to find angle B
angle A + angle B + angle C = 180
But angle B = 2 Angle A
x + 2x + 90 = 180
3x + 90 = 180
3x = 180-90
x = 30°
Angle B = 2 × 30 = 60°
Sin 60 = x/ 24
0. 8660 = x/24
Cross multiply
x = 24 × 0. 8660
x = 20. 78cm
We have the angle of A in the given triangle to be divide into two by the bisector, angle A = 15°
To find line AL, we use
Cos = adjacent/ line AL
Cos 15 = 20. 78/ line AL
Line AL = 20. 78/ cos 15
Line AL = 20. 78 / 0. 9659
Line AL = 21. 51 cm
Thus, the value of line AL is 21. 51cm
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Geometry
Help pls list steps so I can learn :)
Answer: [tex]\frac{25\pi}{4}[/tex]
Step-by-step explanation:
The area of the entire circle is [tex]\pi(5^2)=25\pi[/tex].
The area of a quarter of the circle is thus [tex]\frac{25\pi}{4}[/tex]
And a certain watery an urn contains balls number 1 to 34 from this are in five balls are chosen randomly without replacement for a one dollar bed a player chooses one set of phone numbers to Wayne all five numbers match match those shows it from the urn the order in which the balls or select it doesn’t matter what is the probability of winning the lottery with one ticket
The probability of winning the lottery with one ticket is mathematically given as
P(W)=2.99484408*10^{−8}
What is the probability of winning the lottery with one ticket?Generally, the equation for the probability is mathematically given as
P(1st ball)=1/34
one ball drawn remain
34-1=33
P(2nd ball)=1/33
In conclusion, the probability of winning the lottery with one ticket is
P(W)=1/34*1/33*1/32*1/31*1/30
P(W)=2.99484408*10^{−8}
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Question
Determine an angle between 0° and 360° that is coterminal to an angle with measure of 1524°.
Enter your answer below without a degrees symbol - just enter the numeric answer.
Answer: 84°
Step-by-step explanation:
On a unit circle, coterminal angles are angles that are in the opposite position of the asked angle. 1524° revolves around 127/15π times across the entire unit circle.
84° is the only positive coterminal angle between 0 and 360 that is in the opposite position of 1524°.
Keep in mind, that there are more coterminal angles, namely 444°, 804°, 1164°, and 1524° itself, but they are outside of the range of 0 and 360 degrees.
Find the measure of the angle indicated in bold
The measure of the angles in bold are as follows;
25. 90° and 90°
26. 60° and 60°
How to find angles?When two parallel lines are cut by a transversal , angle relationship are formed. They are alternate angles, corresponding angles etc.
Therefore,
x + 96 + x + 96 = 180
2x = 180 - 192
2x = -12
x = -6
Hence, the angles are 90 and 90 degrees.
6x = 5x + 10(corresponding angles)
6x - 5x = 10
x = 10
Therefore, the angles are 60 degrees and 60 degrees
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