Answer:
b. 4.9 × 1011
Step-by-step explanation:
Using scientific notation is similar to expressing in standard form. Given that (7 × 105)2
We open the parenthesis. This may first be expressed as
7² × 10⁽⁵⁾²
Then expand,
= 49 × 10¹⁰
To put in scientific notation, 49 = 4.9 × 10
Hence the expression becomes
= 4.9 × 10 × 10¹⁰
Using the laws of indices
= 4.9 × 10¹¹ in scientific notation
Answer:
4.9 × 1011
Step-by-step explanation:
I did it in grandpoint
An amount was invested at r% per quarter. What value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
25.75 % interest rate
Step-by-step explanation:
Given:
Amount was invested = r% per quarter
Amount invested = P
Rate of interest = r % per quarter
Time (n) = 4 Quarters
Computation:
A = P(1 + r/100)ⁿ
According to question.
⇒ A = P + 1.5P = 2.5P
⇒ 2.5P = P(1 + r/100)⁴
⇒ 2.5 = (1 + r/100)⁴
⇒ 1 + r/100 = 1.2575
⇒ r/100 = 0.2575
⇒ r = 25.75
25.75 % interest rate
Two number cubes are rolled for two separate events:
Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Complete the conditional probability formula for event B given that event A occurs first by writing A and B in the blanks:
P ( _a0 | _a1) = P ( _a2 ∩ _ a3)
___________
P ( _a4)
Answer: [tex]\bold{P(B|A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{11}{30}}[/tex]
Step-by-step explanation:
The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)
[tex]P(B|A)=\dfrac{P(B\cap A)}{P(A)}[/tex]
P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)
(2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)
(3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)
(4, 5), (4, 4), (4, 3), (4, 2), (4, 1)
(5, 4), (5, 3), (5, 2), (5, 1)
(6, 3), (6, 2), (6, 1)
= 30
P(B) = (1, 2), (2, 1) sum = 3
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) sum = 6
(3, 6), (4, 5), (5, 4), (5, 4), (6, 3) sum = 9
(6, 6) sum = 12
= 12
P(A ∩ B) = (1, 2), (2, 1)
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
(3, 6), (4, 5), (5, 4), (5, 4), (6, 3)
= 11
Solve the inequality -1/2x -3 ≤ -2.5
Answer:
x ≥-1
Step-by-step explanation:
-1/2x -3 ≤ -2.5
Add 3 to each side
-1/2x -3+3 ≤ -2.5+3
-1/2x ≤ .5
Multiply each side by -2, remembering to flip the inequality
-2 * -1/2x ≥ 1/2 * -2
x ≥-1
Solving for a Confidence Interval: Algebra 2 points possible (graded) In the problems on this page, we will continue building the confidence interval of asymptotical level 95% by solving for p as in the video. Recall that R1,…,Rn∼iidBer(p) for some unknown parameter p , and we estimate p using the estimator p^=R¯¯¯¯n=1n∑i=1nRi.
As in the method using a conservative bound, our starting point is the result of the central limit theorem:
In this second method, we solve for values of P that satisfy the inequality volves penat che non esito para polcomp R -P
To do this, we manipulate - ulate | " Vp(1-) 5 < 90/2 into an inequality involving a quadratic function App + Bp+C where A > 0, B, C la/2 into an inequality in depend on 13, 4a/2, and R. Which of the following is the correct inequality?
(We will use find the values of A, B, and C in the next problem.)
1. Ap^2 + Bp + C<0 where A >0.
2. Ap^2 + Bp+C>Owhere A >0.
Let P1 and P2 with 0
a. (P P2)
b. P
Answer:
Step-by-step explanation:
1) The given inequality is
[tex]|\sqrt{n} \frac{(\bar R_n-p)}{\sqrt{p(1-p)} } |<q_{\alpha /2}| \\\\ \to(\frac{(\sqrt{n} \bar R_n-p)}{\sqrt{p(1-p)} })<q^2_{\alpha /2}[/tex]
[tex]\to n( \bar R _n - p)^2<p(1-p)q^2_{\alpha /2}[/tex]
[tex]\to n\bar R +np^2-2nR_np<q^2_{\alpha /2 p- q^2_{\alpha /2}p^2[/tex]
Arranging the terms with p² and p, we get
[tex]p^2(n+q^2_{\alpha /2)-p(2n \bar R _n+q^2_{\alpha / 2})+n \bar R ^2 _n <0[/tex]
Hence, the inequality is of the form
Ap² + Bp + c < 0
2. A quadratic equation of the form
Ap² + Bp + c < 0 with A > 0 looks like
Check the attached image
The region where the values are negative lies between p₁ and p₂ ...
The p₁ < p < p₂
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
7.1
Step-by-step explanation:
d = sqrt(7^2 + -1^2)= sqrt(50)=7.1
Answer:
by using distance formula
putting values
d=√(-1-6)²+(-4--5)²
d=√(-7)²+(1)²
d=√49+1
d=√50
d=5√2=7.1
When Ravi brought 3 friends to his house after school, his mother gave them a box of pretzels and a box of crackers. She told them to share the snacks equally among themselves and to give her any that were leftover.
The boys opened the boxes and found a total of 26 pretzels and 35 crackers.
How many pretzels and crackers did the boys give to Ravi's
Answer:
6 pretzels and 8 crackers
Step-by-step explanation:
Since his mom told him to give her the remaining, 6*4= 24 giving to his mom 2 pretzels and 8*4=32 so he has to give his mom 3 crackers. This way him and his friends have the same amount of snacks.
Hope you find it useful. Good night
How many 3-letter codes can be formed if the second letter must be a vowel (a, e, i, o, u)?
Answer:
3,380 combinations
Step-by-step explanation:
26*5*26= 3,380
Answer:
3380
Step-by-step explanation:
Since there are 26 letters, it would be
26*5*26
This is 3380
Solve 5x^2+3x-4=0 for x using quadratic formula
Answer:
Step-by-step explanation:That would be the answer
How can you use mathematics to help scientists explore Martian Craters ?
Answer:
Mathematics could make scientists to have a preliminary understanding of the dimensions, perimeters, areas and volumes of different craters on Mars.
Step-by-step explanation:
Martian Craters are series of craters formed on the surface of Mars. The study of a planets crater gives an understanding of the properties of matter that lies under the crater.
Mathematics can be applied to determine the dimensions, perimeter, area and volume of the features of a crater using appropriate conversions and theorems.
The Pi in the sky theorem can be applied to determine the area and perimeter, even volume of different craters on the Mars surface. Also, eingenfunction expansion theorem gives a preliminary knowledge of the craters.
By measurements and conversions processes, the features of Martian crater could be studied from images.
2(x+b)= ax + c
In the equation above, a, b, and c are constants. If
the equation has infinitely many solutions, which of
the following must be equal to c?
Α) α
B) 6
C) 2a
D) 26
6500 rounded to the nearest thousand is __. Enter your answer without commas
Answer:
7000
Step-by-step explanation:
If the hundreds place is higher than 5, then add 1 to the thousands place.
Joseph places $5,500 in a savings
account for 30 months. He earns $893.75
in interest. What is the annual interest
rate?
Answer: About 6.2%
Step-by-step explanation:
He starts with 5500 and gains 893.75 in 2.5 years.
The equation is then 5500*(x)^2.5 = 5500+893.75, or
5500*x^2.5 = 6393.75.
x is about 1.0621, or about 6.2% because it's interest.
Hope that helped,
-sirswagger21
Answer: 137.5%
Step-by-step explanation
Suppose Carol Danvers invested $1,000 into an account paying 6% annual interest compounded
annually.
How much is in her account at the end of one year?
Answer:
$ 1,060.00
Step-by-step explanation:
A = $ 1,060.00
A = P + I where
P (principal) = $ 1,000.00
I (interest) = $ 60.00
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
A random sample of 18 graduates of a certain secretarial school typed an average of 80.6 words per minute with a standard deviation of 7.2 words per minute. Assuming a normal distribution for the number of words typed per minute, compute the 95% prediction interval for the next observed number of words per minute typed by a graduate of the secretarial school.
Answer: ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 80.6 words per minute
Standard deviation r = 7.2
Number of samples n = 18
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
80.6+/-1.96(7.2/√18)
80.6+/-1.96(1.697056274847)
80.6 +/- 3.33
= ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
Solve 4x+5≥-23. show your work
Answer:
x≥-7
Step-by-step explanation:
4x+5≥-23
Subtract 5 from each side
4x+5-5≥-23-5
4x≥-28
Divide each side by 4
4x/4≥-28/4
x≥-7
Answer:
X≥-7
Step-by-step explanation:
Step 1: Subtract 5 from both sides.
4x+5-5≥-23-5
4x ≥-28
Step 2: Divide both sides by 4.
4x/4 ≥-28/4
X ≥-7
Maddie is packing moving boxes. She has one 3 cubic-foot box and one 6 cubic-foot box. How many cubic feet of clothing can she fit in the two boxes?
8 9 10 12
Answer:
She can fit 9 cubic feet of clothing in the two boxes.
Step-by-step explanation:
She can fit a total of 3 cubic feet of clothing in one box, and the other she can fit a total 6 cubic feet.
3 + 6 = 9
Answer:
9 cu ft.
Step-by-step explanation:
That is the sum of the capacities of the 2 boxes
= 3 + 6
= 9 cu ft.
Please help this is urgent!
Answer:
Isosceles
Obtuse
Step-by-step explanation:
1) When two sides of a triangle are the same length, the triangle is an isosceles triangle.
2) When one angle of the triangle is greater than 90 degrees, the triangle is an obtuse triangle.
I hope this helps! Have a great day!
Answer:
Isosceles, obtuse
Step-by-step explanation:
There are three types of triangles based on their sides:
Equilateral: a triangle with 3 equal sidesIsosceles: a triangle with 2 equal sidesScalene: a triangle with no equal sidesThis triangle here as sides of 28 cm, 16 cm, and 16 cm
This triangle has two equal sides of 16 cm, indicating it is an isosceles triangleThere are three types of triangles based on their angles:
Acute: when all angles are less than 90° Right: when the triangle has one angle that is 90° Obtuse: when one of the angles is greater than 90°This triangle has angles of 26°, 26°, and 128°
This triangle has one angle that is greater than 90° → 128°, indicating that this is an obtuse triangleWhich expression best represents the situation?
Select the expression that best matches the scenario.
O4 + x + 3
4(x + 3)
4.3
4x + 3
Tyson bought a burger for himself and
each of his 3 friends. He left a tip of $3.
Which expression could represent
the amount of money Tyson spent?
Explain your thinking.
Help plz
Answer:509
Step-by-step explanation:600
A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.
Answer:
0.102
Step-by-step explanation:
The number of defective modems in the inventory is 20% * 30 + 8% * 0.50 =10 (out of 80)
Note that the number of defectives in the inventory is fixed i.e. we are told that there is 1/8 probability that a modem in the inventory is defective, but rather that exactly 1/8 of all modems are defective.
The probability that exactly two modems in a random sample of five are defective is :
(10↓2)(70↓3) / (80↓5) = 0.102
Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?
y = -2
y = x + 2
y = x + 3
y=x-5
Answer:
y = x - 2
Step-by-step explanation:
y = x + b
3 = 5 + b
y = x - 2
We can use the slope intercept form of a line.
y = mx+b where m is the slope and b is the y intercept
y = 1x +b
Substitute the point into the equation
3 = 1*5+b
3 = 5+b
Subtract 5 from each side
3-5 = 5+b-5
-2 =b
y = x-2
Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 18 specimens of a particular species, 5 resprouted after fire. Estimate with 99.5% confidence the proportion of all shrubs of this species that will resprout after fire.
Answer:
The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 18, \pi = \frac{5}{18} = 0.2778[/tex]
99.5% confidence level
So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 - 2.81\sqrt{\frac{0.2778*0.7222}{18}} = -0.01 = 0[/tex]
We cannot have a negative proportion, so we use 0.
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 + 2.81\sqrt{\frac{0.2778*0.7222}{18}} = 0.5745[/tex]
The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).
What’s the correct answer for this?
Answer:
(2,-2)
Step-by-step explanation:
In the attached file
Solve x for the diagram below.
Answer:
20°
Step-by-step explanation:
These angles add up to 90° so we have:
x + 2x + x + 10 = 90
4x + 10 = 90
4x = 80
x = 20°
Rachel owns as twice as many beanie babies as Kaye. Alexia owns 1/3 as many beanie babies as Rachel. If Kaye owns 63 beanie babies,how many does Alexia owns?
Answer:
42
Step-by-step explanation:
Let the number of beanie babies Kaye has be x
according to question
Rachel owns as twice as many beanie babies as Kaye
number of beanie babies Rachel has : 2*x = 2x
Also,
Alexia owns 1/3 as many beanie babies as Rachel
number of beanie babies Alexia has : 1/3(2x) = 2x/3
It is given that Kayes has 63 beanie babies
thus x = 63
Thus,
Number of beanie babies Alexia has = 2x/3 = 2*63/3 =2*21 = 42
The table represents an exponential function. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 0.25, 0.125, 0.0625, 0.03125. What is the multiplicative rate of change of the function? 0.2 0.25 0.5 0.75
Answer:
0.5 or C on edge2021
Step-by-step explanation:
The multiplicative rate of change of the function will be:
0.5What is a Multiplicative rate of change?The multiplicative rate of change is the common factor that the numbers can be multiplied with to get the succeeding figures.
For instance, if 0.25 is multiplied by 0.5, the result will be 0.125. Also, if 0.125 is multiplied by 0.5, the result will be 0.0625.
Learn more about the multiplicative rate of change here:
https://brainly.com/question/4319809
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Use the 95% rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values. A bell-shaped distribution with mean 1050 and standard deviation 7.
The interval is to:_______.
Answer:
Intervals = (1,064) , (1,036)
Step-by-step explanation:
Given:
Use 95% method
Mean = 1,050
Standard deviation = 7
Find:
Intervals.
Computation:
95% method.
⇒ Intervals = Mean ± 2(Standard deviation)
⇒ Intervals = 1,050 ± 2(7)
⇒Intervals = 1,050 ± 14
⇒ Intervals = (1,050 + 14) , (1,050 - 14)
⇒ Intervals = (1,064) , (1,036)
The Intervals = (1,064) , (1,036)
Given that:
Use 95% methodMean = 1,050Standard deviation = 7Based on the above information, the calculation is as follows:
Intervals = Mean ± 2(Standard deviation)
Intervals = 1,050 ± 2(7)
Intervals = 1,050 ± 14
Intervals = (1,050 + 14) , (1,050 - 14)
Intervals = (1,064) , (1,036)
Learn more: https://brainly.com/question/1368131?referrer=searchResults
A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply.
The area of the rectangle is 88 square inches.
The equation x(x – 3) = 44 can be used to solve for the dimensions of the triangle.
The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.
The triangle has a base of 11 inches and a height of 8 inches.
The rectangle has a width of 4 inches.
Answer:
⬇⬇⬇⬇⬇⬇
⬇⬇⬇⬇⬇⬇
Step-by-step explanation:
1, 3, 4
proof below
(1) The area of the rectangle is 88 square inches
(3) The equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.
(4) The triangle has a base of 11 inches and a height of 8 inches.
Area of the rectangle
Area of a rectangle is the sum of the area of two equal right triangle.
Area of rectangle = 2(area of right triangle)
Area of rectangle = 2(44 sq inches) = 88 sq inches
Total area of the triangle with respect to length and width of the rectangleLet the length = x
then the width becomes, x - 3
Area = x(x - 3) = 88
x² - 3x = 88
x² - 3x - 88 = 0
x = 11
width = 11 - 3 = 8
Thus, the statements that are true include;
The area of the rectangle is 88 square inchesThe equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.The triangle has a base of 11 inches and a height of 8 inches.Learn more about area of rectangle here: https://brainly.com/question/25292087
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Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an average speed of 54 mph. How long does it take for the van to catch up with the storm? How far have they driven? (Hint: we can let our two variables be x= distance and t= time. Additionally, [speed x time= distance]. Won’t the van catch up when the distances are equal?
Please make it easy to understand your answer :)
Answer:
Time = X = 37.14 minutes
Distance they covered= 33.42 miles.
Step-by-step explanation:
Distance= speed * time
And the distance traveled by the two need to be equal.
Speed of storm = 33 mph
Speed of van = 54 mph
But storm is 13 miles away from van.
So
54*x = 33*x+ 13
54x-33x = 13
21x = 13
X= 0.62 hours
X = 37.14 minutes
54 *0.62= 33.42 miles.
Can someone please help me fast
Answer:
x = 3.5
Step-by-step explanation:
Since the triangles are similar we can use ratios to solve
4 7
------ = ------
(4+2) ( 7+x)
Using cross products
4(7+x) = 7*(4+2)
Distribute
28+4x = 42
Subtract 28 from each side
4x = 42-28
4x= 14
Divide by 4
4x/4 = 14/4
x = 7/2
Which choice is equivalent to the expression below?
root-81
A. 9i
B. i root9
C. root9i
D. -9
E. -root9
Answer: B
Step-by-step explanation: