Answer: The probability of getting 100 % on the quiz is 0.0625.
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Step-by-step explanation:
Since we have given that
Number of true-false questions = 4
Number of chances of answer = 2
1) True,
2) False
Probability of getting correct answer is given by
[tex]\frac{1}{2}[/tex]
Probability of getting 100% on the quiz by randomly guessing the answer to all 4 questions is given by
[tex]\frac{1}{2}^4\\\\=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\\\=\frac{1}{16}\\\\=0.0625[/tex]
Hence, The probability of getting 100 % on the quiz is 0.0625.
In the equation y = mx + b, b represents:
A. slope
B. rise
C. y - intercept
D. x - intercept
Given F(x) = log8 x, find F(64). ...?
Answer:
[tex]F(64)=2[/tex]
Step-by-step explanation:
Given the funtion:
[tex]F(x)=log_8(64)[/tex]
We need to find the value of the function at x=64:
[tex]F(64)=log_8(64)= z[/tex]
Where z is the value we are trying to find. In order to find z, let's use the definition of the base of a log:
[tex]log_xy=z\Rightarrow x^z=y[/tex]
So:
[tex]8^z=64[/tex]
Express [tex]8^z[/tex] as:
[tex]2^{3z}[/tex]
And express 64 as:
[tex]2^6[/tex]
Which leads to:
[tex]2^{3z}=2^6[/tex]
Equate exponents of 2 on both sides:
[tex]3z=6[/tex]
Solving for z:
[tex]z=\frac{6}{3} =2[/tex]
Therefore:
[tex]F(64)=log_8(64)= z=2[/tex]
Absolute value?? |x+2|=10
Answer:
x=8 or just x+2=10
Step-by-step explanation:
if you wanted to know this without absolute value, its still x+2=10. if you wanna know what 'x' is, its 8.
what is 200 times 16?
a scale model of a statue is 7 inches tall. The scale of the model is 1in./1.5ft. what is the actual height of the statue?
Traveling at 45 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 240 miles from Orlando to Miami?
a. 5
b. 195
c. 285
d. 320
Let U = {21, 22, 23, ..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, ..., 39}, and D = {22, 24, 26, 28, ..., 40}.
Use the roster method to write the following set.
11) Aʹ
The complement of set A with respect to the universal set U (A') is {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}, which contains all elements in U that are not in set A.
Explanation:The student is asked to use the roster method to write the set A', which represents the complement of set A with respect to the universal set U. The set A' consists of all elements in the universal set U that are not in set A.
First, we list all the elements of the universal set U, which are {21, 22, 23, ..., 40}. Set A contains {21, 22, 23, 24, 25}. To find A', we remove the elements of A from U, resulting in A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}.
Final answer:
The set A' includes all numbers from 26 to 40 in the universal set U, which are not included in set A.
Explanation:
To find the set A' or the complement of set A in the universal set U, we need to list all the elements in U that are not in A. Given that the universal set U consists of the numbers 21 through 40, and the set A includes the numbers 21, 22, 23, 24, and 25, we can determine A' by subtracting these from U.
The roster method simply lists out all of the elements. Doing so for A' yields the following:
A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}
These are all the numbers in U that are not in A.
What is the product of written in simplest form? 7/10 divided by 5/6
If a road has a 4% grade and rises 200 feet, what is the run?
Answer:
5000
Step-by-step explanation:
400 ÷ 4% = 5000
Which set of ordered pairs in the form (x,y) does not represent a function of x?
A {(-1,2),(3,-2),(0,1),(5,2)}
B. {(-1,2),(3,2),(-2,2),(0,2)}
C. {(-1,2),(3,-2),(0,1),(3,5)}
D. {(-1,2),(2,3),(3,-2),(-2,0)}
Answer:
Option C
Step-by-step explanation:
A function is a relation that does not contain two pairs with same first component.
Option A
{(-1,2),(3,-2),(0,1),(5,2)} is a function, since there are no two pairs with the same first component.
option B
{(-1,2),(3,2),(-2,2),(0,2)} is a function, since there are no two pairs with the same first component.
option C
{(-1,2),(3,-2),(0,1),(3,5)} is not a function, since there are two pairs with the same first component i.e, 3
OptionD
{(-1,2),(2,3),(3,-2),(-2,0)} is a function, since there are no two pairs with the same first component.
So, {(-1,2),(3,-2),(0,1),(3,5)} is the required answer.
Which statement is correct?
A horizontal line has no slope.
A vertical line has a slope of zero.
A line that rises from left to right has a positive slope.
A line that falls from right to left has a negative slope.
Answer:
A line that rises from left to right has a positive slope
Step-by-step explanation:
Verify each statement
case A) A horizontal line has no slope
The statement is False
Because a horizontal line has a slope equal to zero
case B) A vertical line has a slope of zero
The statement is False
Because a vertical line has a undefined slope
case C) A line that rises from left to right has a positive slope
The statement is True
case D) A line that falls right to left has a negative slope
The statement is False
Because a is a positive slope
Find the values of x and y drawing not to scale
Part 1)
In this problem we know that
[tex]4y\°+112\°=180\°[/tex] ------> by supplementary angles
solve for y
[tex]4y\°=180\°-112\°[/tex]
[tex]y=68\°/4[/tex]
[tex]y=17\°[/tex]
Part 2)
In this problem we know that
[tex]7x+7=112\°[/tex] ------> by vertical angles
solve for x
[tex]7x=112\°-7\°[/tex]
[tex]x=105\°/7[/tex]
[tex]x=15\°[/tex]
therefore
the answer is the option A
[tex]x=15\°, y=17\°[/tex]
Jen is making a frame to stretch a canvas over for a painting. She nailed four pieces of wood together at what she believes will be the four vertices of a square. How can she be sure that the canvas will be a square?
a. All four of the pieces of wood are the same length & at least two interior angles are congruent.
b. At least two pieces of wood are the same length & at least two interior angles are congruent.
c. At least two pieces of wood are the same length & all four interior angles are congruent.
d. All four of the pieces of wood are the same length & all four interior angles are congruent.
If a and b are positive numbers, find the maximum value of f(x)=x^a*(1-x)^b, 0 less than or equal to x less than or equal to 1.
Your answer may depend on a and b. What is the maximum value? ...?
They are offering chocolate, vanilla, strawbrry ice cream. and they ar also can choose from toppings chocolate syrup, sprinkles, caramel, or whipped cream. how many sundae combinations ar possible
Final answer:
By using the counting principle and multiplying the choices for ice cream flavors (3) by the choices for toppings (4), we find there are 12 possible sundae combinations.
Explanation:
To determine the number of possible sundae combinations with the given choices, we can use the counting principle. We multiply the number of options for each category. In this case, there are three choices for ice cream flavors (chocolate, vanilla, and strawberry) and four choices for toppings (chocolate syrup, sprinkles, caramel, and whipped cream).
Since a sundae consists of one ice cream flavor and one topping, we simply multiply the number of options for ice cream by the number of options for toppings.
3 ice cream flavors × 4 toppings = 12 possible combinations.
Therefore, there are 12 unique sundae combinations a customer can choose from.
A square has an area of 80 square inches. What is the length of a side of the square, in inches?
To find the length of a side of a square with an area of 80 square inches, we take the square root of the area. This results in each side of the square being approximately 8.944 inches long.
Explanation:The question is asking to find the length of a side of a square that has an area of 80 square inches. In geometry, the area of a square is calculated by squaring the length of one side. Therefore, to find the length of a side when you know the area, you need to take the square root of the area.
So, in this case, we take the square root of 80. Using a calculator, this results in approximately 8.944 inches. Therefore, each side of the square is about 8.944 inches long.
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If you help, please finish the answer, because I really need help. Everyone disappears on me.
A survey by the state health department found that the average person ate 208 pounds of vegetables last year and 125 5/8 pounds of fruit.What fraction of the total pounds of fruit and vegetables do the pounds of fruits represent?
Answer: The fraction of pounds of fruits over total pounds of fruits and vegetables is given by
[tex]\frac{25125}{66724}[/tex]
Step-by-step explanation:
Since we have given that
Total amount of vegetables = 208 pounds
Total amount of fruits is given by
[tex]125\frac{5}{8}\text{ pounds}[/tex]
Total amount of fruits and vegetables is given by
[tex]208+125\frac{5}{8}\\\\=208+\frac{1005}{8}\\\\=\frac{1664+1005}{8}\\\\=\frac{2669}{8}\\\\=333.625\text{ pounds }[/tex]
So, we need to find the fraction of pounds of fruits over the total pounds of fruit and vegetables :
[tex]\frac{\text{Pounds of fruits }}{\text{ total pounds of fruits and vegetables}}\\\\=\frac{\frac{1005}{8}}{333.62}\\\\=\frac{1005}{8\times 333.62}\\\\=\frac{1005}{2668.96}=\frac{25125}{66724}[/tex]
The fraction of the total pounds of fruit and vegetables that fruits represent is approximately 0.377, or 37.7%.
Explanation:To find out what fraction the pounds of fruits represent out of the total pounds of fruits and vegetables, we first need to calculate the total pounds of fruits and vegetables consumed. This is found by adding the pounds of vegetables (208) to the pounds of fruits (125 5/8). So, 208 + 125 5/8 = 333 5/8 pounds.
Now, to determine the fraction, we take the pounds of fruits and divide by the total. Hence, the fraction is given by 125 5/8 ÷ 333 5/8. To divide fractions, we multiply by the reciprocal of the divisor, which gives us (125 5/8) * (8/333) = 0.377 (rounded to three decimal places).
Therefore, fruits represent approximately 0.377, or 37.7% of the total pounds of fruits and vegetables consumed.
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at her job, mary works 4 hours on monday, 3 hours on wednesday, and 6 hours on saturday. her boss adds a $10 bonus to her paycheck, which then totals $120.50. what is mary's hourly pay?
a. $8.50
b. $9.27
c. $5.24
d. $8.05
is y = x an additive Relationship? Explain.
simplest form for 21/49
there are 110 calories per 28.4 grams of cereal X.find how many calories are in 45.44 grams of this cereal
Name the intersection of the planes ACE and CDF
What is the value of x? 18-7x = -20.5
if you found 259 to the nearest hundreds,what is the answer
find (2 × 107) (3 × 104).
Find the radius of a circle with an area of 90 cm^2
What are the solutions to the equation 3(x – 4)(x + 5) = 0?
Answer:
-5, 4
Step-by-step explanation:
the solutions to the equation [tex]3(x - 4)(x + 5) = 0[/tex]
To solve for x we set each factor =0 and solve for x
[tex]3(x-4)=0[/tex]
divide each term by 3
[tex](x-4)=0[/tex]
Add 4 on both sides
[tex]x=4[/tex]
[tex]x+5=0[/tex]
Subtract 5 on both sides
[tex]x=-5[/tex]
So x values are -5 and 4
What is the absolute value of 6?
Answer:
absolute value is 6
9 times as many as 457 is