We need to select at least 754 people for the experiment to estimate the fraction of people who black out at G forces greater than 6 with an error of at most 0.03 and a 95% confidence level.
How to determine how large a sample would be required in order to estimate the fraction of people who black out at 6or more Gs
We can use the formula for the sample size required to estimate a population proportion with a specified margin of error and confidence level:
n = (Z^2 * p * (1-p)) / E^2
where:
Z = the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of 1.96)
p = the estimated population proportion from the earlier study
E = the desired margin of error
Substituting the given values, we get:
n = (1.96^2 * 0.33 * (1-0.33)) / 0.03^2
n = 753.69
Rounding up to the next integer, we need a sample size of 754. Therefore, we need to select at least 754 people for the experiment to estimate the fraction of people who black out at G forces greater than 6 with an error of at most 0.03 and a 95% confidence level.
Learn more about sample size at https://brainly.com/question/30123000
#SPJ1
A man bought two pencils and three biros at a cost of 50, Again he bought three pencils and four biros for 70. find the cost of a pencil and a biro
What is the solution to the equation 3/5x-4-3√7x+8?
A x = -6
B x=-1
C x = 1
D x = 2
The solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
To solve the equation 3/5x - 4 - 3√7x + 8 = 0:
First, simplify the expression by combining like terms:
3/5x - 3√7x + 4 = 0 + 8
3/5x - 3√7x + 4 = 8
Next, move the constant term to the right side:
3/5x - 3√7x = 8 - 4
3/5x - 3√7x = 4
Factor out x from the left side:
x(3/5 - 3√7) = 4
Divide both sides by (3/5 - 3√7):
x = 4 / (3/5 - 3√7)
To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (3/5 + 3√7):
x = 4(3/5 + 3√7) / [(3/5 - 3√7)(3/5 + 3√7)]
x = 12/5 + 12√7/5 / (9/25 - 63/25)
x = 12/5 + 12√7/5 / (-54/25)
x = -10√7/9
Therefore, the solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.
Learn more about equation on:
https://brainly.com/question/27893282
#SPJ9
A container in the shape of a rectangular prism has a height of 2 feet. Its length is four
times its width. The volume of the container is 200 cubic feet. Find the length and width of
the container.
Answer: length = 20 feet and width = 5 feet
Step-by-step explanation: Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.
3. In a sports centre, the ages of 100 people were recorded as follows: Age Under 20 years 20 to 29 years 30 t0 39 years 40 to 59 years 60 years and over Number of people 30 15 12 14 29 Fri, 24 Mar 2023 Angle (i) complete the table above to show the angle for each categ rounded off to the nearest degree. (ii) construct a pie chart using the circle below.
100 people = 360° of circle
For n people, the degree for the circle is (n×360)÷100
30 people = (30×360)÷100 = 108°
15 people = 54°
12 people = 43.2° ≅ 43°
14 people = 50.4° ≅ 50°
29 people = 104.4° ≅ 104°
Which expresion has the greatest value when n is equal to 4
The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.
How do we calculate?To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.
A. 5n = 5(4) = 20
B. n + 30 = 4 + 30 = 34
C. 50 - n = 50 - 4 = 46
D. 80 ÷ n = 80 ÷ 4 = 20
The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n
Learn more about mathematical expression at: https://brainly.com/question/1859113
#SPJ1
Becky ate 7.5 x 10^5 milligrams of rice. Carter ate 3.1 x 10^6 milligrams of rice. who ate more?
Answer:
The Correct answer is Carter
50pts!!!!
Many investors use interest-only loans to buy shares or property. For such loans the principal stays constant and only the interest is paid back each month.
She buys an investment property for $300 000 and borrows the full amount at 7% p.a. simple interest. She rents out the property at $1500 per month and pays $3000 per year in rates and other costs to keep the property.
Find the amount of interest she needs to pay back every month.
Find her yearly income from rent.
By considering the other costs in keeping the property, calculate her overall loss in a year.
she hopes that the property’s value will increase enough to cover any loss she is making. By what percentage of the original price will the property need to increase in value per year?
Step-by-step explanation:
to find the interest she needs to pay back every month, we need to use this formula:
I = PRT/12
in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:
I = (300,000)(7)(1)/12 = $17,500 in interest every month
to find her yearly income from rent, we have to multiply the monthly rent by 12
1500 × 12 = $18,000
to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000
she said that she hopes the property's value will increase to cover the loss she made.
to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as
Percentage increase = (difference in increase/Original price) × 100
so
percentage increase = (15000/300000) × 100 = 5%
so the property needs to increase in value by at least 5% per year to cover the loss.
The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.
Explanation:First, let's calculate the monthly interest she needs to pay. 7% of $300,000 is $21,000 for a year. To find the monthly interest, we divide this by 12, resulting in $1750.Her yearly income from rent is $1500 multiplied by 12, giving us $18,000.To calculate her overall loss, we add the yearly interest and the costs to keep the property, then subtract the yearly rent income. So, $21,000 + $3000 - $18,000 = $6000 loss per year.Lastly, to find out by what percentage the property value needs to increase, we divide the loss by the original price and multiply by 100, giving us 2% increase per year.Learn more about Interest and Profit Calculation here:https://brainly.com/question/32651816
#SPJ2
The supply and demand for a product are related to price by the following equations, where y is the price, in dollars, and x is the number of units, in thousands. Find the equilibrium point for this product.
y=300+40x
y=9300-50x
helpp..
Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:
300 + 40x = 9300 - 50x
Simplifying and solving for x:
90x = 9000
x = 100
Now that we know x, we can use either equation to find y:
y = 300 + 40(100) = 4300
So the equilibrium point is when x = 100 and y = 4300.
Step-by-step explanation:
Please help me please tysm and have a great day :)
Answer:
mean: 20mins
Step-by-step explanation:
add them all together to get 240
then divide by how many there are
240÷12=20
so the mean is 20mins
solve for r if $425.83=400(1+r)^5 ? (show explanation please)
Answer: 0.0295
Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.
Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:
$1+r=\sqrt[5]{1.064575}$.
Subtracting 1 from both sides gives $r\approx 0.0295$.
Therefore, your answer would be 0.0295.
60°
y
Find the value of y.
A. y = 2
B.
4√√3
3
y = 4
C.
D. y = 4√3
8
30°
The value of y is 4, so the answer is option A: y = 4.
What is trigonometric ratios ?
Trigonometric ratios are mathematical relationships between the angles and sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.
Using the given diagram, we can use the trigonometric ratios to find the value of y.
First, we can find the length of the side opposite the 30-degree angle by using the sine ratio:
sin(30°) = opposite/hypotenuse
sin(30°) = y/8
y/8 = 1/2
y = 8/2
y = 4
Therefore, the value of y is 4, so the answer is option A: y = 4.
To know more about trigonometric ratios visit:
https://brainly.com/question/1201366
#SPJ1
Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.
Answer: The formula for compound interest is:
A = P(1 + R/100)^t
where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.
Here, P = Rs. 3,500, R = 8%, and t = 2 years.
So, the amount after 2 years will be:
A = 3,500(1 + 8/100)^2
= 3,500(1.08)^2
= 3,892.32
Therefore, the compound interest for 2 years will be:
CI = A - P
= 3,892.32 - 3,500
= 392.32
Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.
Step-by-step explanation:
Could someone help me find the answers and show me how they got it it’s a review for a quiz I have to take for tomorrow
Area of composite shape = 12 + 9
= 21 cm²
How to solve
Area of composite shapes:
13) Figure 1:
Figure1 is a rectangle.
l = 4 cm & w = 2 cm
Area of figure1 = l * w
= 4 * 2
= 8 cm²
Figure2:
Figure2 is a parallelogram
base = b = 4 cm
h = 4 cm
Area of figure2 = b * h
= 4 * 4
= 16 cm²
Area of composite shape = 8 + 16
= 24 cm²
14) Figure1:
Figure 1 is a trapezium. a & b are parallel sides and h is the height
a = 4 cm ; b = 6 cm; h = 4 -2 = 2 cm
Figure2:
Figure2 is a rectangle. l = 6 cm ; w = 2 cm
Area of figure2 = 6*2
= 12 cm²
Area of composite shape = 10 + 12
= 22 cm²
15) Figure 1 & figure 2:
Figure 1 and figure 2 are congruent triangles
base = b = 3 cm & h= 4 cm
= b *h
= 3 * 4
= 12 cm²
Figure3:
Figure 3 is a square.
side = 3 cm
Area of figure3 = side *side
= 3 * 3
= 9 cm²
Area of composite shape = 12 + 9
= 21 cm²
Read more about area here:
https://brainly.com/question/2607596
#SPJ1
carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
Learn more about rectangle here,
https://brainly.com/question/25292087
#SPJ9
4)
Northbrook Middle School surveyed 325 students to learn more about their after-schoo
activities. They found that 90 students are in a club and play a sport. 140 total students
play a sport and 200 total students are in a club. Construct a two-way relative freques
table summarizing the data.
Plays a Sport
In a Club
Not In a Club
Total
Doesn't Play a
Sport
Total
Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).
What is frequency?Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.
90 students are in a club and play a sport.
140 total students play a sport.
Therefore, 140 - 90 = 50 students play a sport but are not in a club.
The total number of students who play a sport is 140 + 50 = 190.
200 total students are in a club.
Therefore, 200 - 90 = 110 students are in a club but do not play a sport.
The total number of students who do not play a sport is 325 - 190 = 135.
The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.
This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.
To know more about histograms, visit:
https://brainly.com/question/30354484
#SPJ1
Divide and give your answer as a decimal. Round your answer to the nearest thousandth (3 digits behind the decimal).
2/9
Answer:
0.222
Step-by-step explanation:
2 divided by 9 is:
0.222 (rounded to the nearest thousandth)
find the factors to this polynomials i need help SHOW YOUR WORK.
Answer:
hope this will help you...
In order to develop a more appealing cheeseburger, a franchise uses taste tests with 11 5 different buns, 3 different cheeses, 4 types of lettuce, and types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?
It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.
Find the equation of the linear function
represented by the table below in slope-intercept
form.
X: -3,1,5,9
y: -8,0,8,16
By answering the presented question, we may conclude that As a result, the linear function denoted by the table is y = 2x - 2.
what is slope?A line's slope shows how steep it is. A mathematical equation for the gradient is referred to as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of vertical change (rise) to horizontal change between two points (run). The slope-intercept form of an equation is used to represent the equation of a straight line, which is written as y = mx + b. The y-intercept is located where the line's slope is m, b is b, and (0, b). The slope and y-intercept of the equation y = 3x - 7 are two examples (0, 7). The line's slope is m. b is b at the y-intercept, and (0, b).
To obtain the slope and y-intercept of a linear function in slope-intercept form, we must first establish the slope and y-intercept.
With two locations on the line, we can first determine the slope. Let us start with the first and last points in the table:
slope = (y change) / (change in x)
slope = (16 - (-8)) / (9 - (-3))
slope = 24 / 12
slope = 2
We can now use the slope and one of the points to get the y-intercept. Let's take the point (1, 0) as an example:
y = mx + b 0 + b b = 2(1) + b b = -2
Hence the linear function's slope-intercept equation is:
y = 2x - 2
As a result, the linear function denoted by the table is y = 2x - 2.
To know more about slope visit:
https://brainly.com/question/3605446
#SPJ1
Write an absolute value equation that has the following solution set.
-8 and -2
Thank you!
The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3
What is an absolute value equation?
An absolute value equation can be written as |expression| = value
To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.
We can write,
|x + 5| = 3
To solve for x, we have two cases,
Case 1: x + 5 is positive
If x + 5 is positive, then the equation becomes x + 5 = 3
Solving for x,
x = -2
This matches one of the solutions we want.
Case 2: x + 5 is negative
If x + 5 is negative, then the equation becomes -(x + 5) = 3
Solving for x,
x = -8
This also matches the other solution we want.
Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.
Learn more about absolute value here,
https://brainly.com/question/24368848
#SPJ9
When two sample means are significantly different
Group of answer choices
The pooled variance estimate should not be used
The difference is too great to attribute to chance
The corresponding population means are significantly different
The difference is of practical importance
When two sample means are significantly different, "the difference is too great to attribute to chance".
What is statistical significance?The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).
Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.
Learn more about statistical significance here:
https://brainly.com/question/29663617
#SPJ1
ii) The door is 0.9 m wide and 2.1 m high. Each of the four windows is 1.5 m wide and 1.2 m high work out the toral area of the door and the four windows
Answer: The area of the door can be calculated as:
Area of door = width x height
= 0.9 m x 2.1 m
= 1.89 square meters
The area of one window can be calculated as:
Area of window = width x height
= 1.5 m x 1.2 m
= 1.8 square meters
Since there are four windows, the total area of the four windows is:
Total area of four windows = 4 x Area of window
= 4 x 1.8 square meters
= 7.2 square meters
Therefore, the total area of the door and the four windows is:
Total area = Area of door + Total area of four windows
= 1.89 square meters + 7.2 square meters
= 9.09 square meters
Hence, the total area of the door and the four windows is 9.09 square meters.
Step-by-step explanation:
Given f’(x)=4x-3 compute f(5)-f(-1)
Answer:
To solve this problem, we need to integrate the derivative f'(x) to obtain the function f(x).
∫f'(x) dx = ∫(4x - 3) dx
f(x) = 2x^2 - 3x + C
where C is the constant of integration.
To find the value of C, we need to use the fact that f(0) = 5. Substituting x = 0 into the above equation, we get:
f(0) = 2(0)^2 - 3(0) + C = C
Therefore, C = 5.
Hence, the function f(x) is:
f(x) = 2x^2 - 3x + 5
Now, we can find f(5) and f(-1) and compute their difference:
f(5) - f(-1) = (2(5)^2 - 3(5) + 5) - (2(-1)^2 - 3(-1) + 5)
f(5) - f(-1) = (50 - 15 + 5) - (2 + 3 + 5)
f(5) - f(-1) = 35 - 10
f(5) - f(-1) = 25
Therefore, f(5) - f(-1) = 25.
The expression 12x +8 is equivalent to the expression a(bc+c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4). Which statement best explains whether the students answer is correct or incorrect
The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
What is expression?Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.
This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.
To learn more about expression
https://brainly.com/question/1859113
#SPJ1
Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).
Which statement best explains whether the student's answer is correct or incorrect?
OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).
C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).
OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).
Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero
The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.
Describe Comparison Algebra?Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.
Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.
In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.
The statements that provide support for Chloe's claim are:
A. A<0 because A is to the left of zero.
F. B>0 because B is to the right of zero.
Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.
To know more about expression visit:
https://brainly.com/question/6321768
#SPJ9
Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
The total net amount the supermarket owes the wholesaler for the order is $231.31.
What does discount mean?A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.
According to the given informationTo find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.
The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:
Discounted cost = List price - (Discount rate x List price)
For the soup, the discounted cost per case is:
$18.90 - (0.39 x $18.90) = $11.51
For the baked beans, the discounted cost per case is:
$33.50 - (0.39 x $33.50) = $20.42
Now we can calculate the total net amount owed by the supermarket to the wholesaler:
Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)
Total net amount = (13 x $11.51) + (4 x $20.42)
Total net amount = $149.63 + $81.68
Total net amount = $231.31
Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.
To know more about the discount visit:
brainly.com/question/28944081
#SPJ1
Rewrite 6x2 + 2xy + 9x + 3y in factored form. (2x + 3)(3x + y) (2x + y)(3x + 3) (3x + 2)(3x + y) (3x + y)(2x + 1)
Answer:
(3x + y)(2x + 3)
Step-by-step explanation:
Factorizing the expression:6x² = 2 * 3 * x * x
2xy = 2*x * y
Common factor = 2x.
9x = 3 * 3 * x
3y = 3 * y
Common factor = 3
Take out the common factor 2x from the first and second term & take out the common factor 3 from third and fourth term.
6x² + 2xy + 9x + 3y = 2x(3x + y) + 3(3x + y)
= (3x + y)(2x + 3)
) Rewrite as an exponential equation.
log8 1/64 =2
(b) Rewrite as a logarithmic equation.
3 0=1
a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]
b) the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
What is exponential equation?
An exponential equation is one in which the exponent contains a variable.
(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation
log8 1/64 = 2
means that 8 raised to the power of 2 is equal to 1/64:
[tex]8^2 = 1/64[/tex]
Thus, we can write the exponential equation as:
[tex]1/64 = 8^{(-2)}[/tex]
Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]
(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation
[tex]3^0 = 1[/tex]
means that the logarithm of 1 to the base 3 is equal to 0:
log3 1 = 0
Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
To know more about exponential equation visit,
https://brainly.com/question/2456547
#SPJ1
Mohal plans to repaint some classroom bookcases. He has 1 1 /8 gallons of paint. All of the bookcases are the same size and each requires 1/8gallon of paint. How many bookcases will he be able to paint?
Mohal will be able to paint 9 bookcases for the amount of paint.
What is fraction?An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.
Given that, he has 1 1 /8 gallons of paint.
Thus, number of bookcases are:
1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9
Hence, Mohal will be able to paint 9 bookcases for the amount of paint.
Learn more about fraction here:
https://brainly.com/question/10354322
#SPJ1
Prove: DC = 6 units
A
6 units
D
Statements
AD || BC
ZDAC ZBCA
C
?
DC BA
DC = BA
given
alternate interior angles theorem
AC AC
reflexive property of congruence
ZDCA ZBAC alternate interior angles theorem
DC = 6 units
Which step is missing?
B
O A. ADAC
OB. ADCA
O C. ADCA
Reasons
?
CPCTC
definition of congruent sides
substitution property of equality
ABCA by SAS
ABCA by ASA
ABCA by SAS
The missing step in the proof is: D. ADCA
What is the missing step and reason of the proof?In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).
Therefore, we have the following proportional sides:
DC/AC = AC/BC
Given that DC = BA (given statement), we can substitute BA for DC in the proportion:
BA/AC = AC/BC
Now, we can cross-multiply to get:
BA * BC = AC²
Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:
BA * BC = AC * AC
Use the definition of congruent sides to replace BA with DC:
DC * BC = AC * AC
And finally, use the substitution property of equality to replace BC with 6 units (given statement):
DC * 6 = AC * AC
From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.
Learn more about proof at brainly.com/question/30113873
#SPJ1