Option C: The relationship between the statement cannot be determined.
What is Conditional statement?
Two independent statements can be related to each other in a logic structure called a conditional statement.
The first statement is presented with “if,” and is referred to as the hypothesis.
The second statement is linked with “then”, and is known as the conclusion.
The notation associated with conditional statements typically uses the variable p for the hypothesis statement, and q for the conclusion.
p → q
Explanation for the answer:
The converse statement is notated as q→p (if q, then p). The original statements switch positions in the original “if-then” statement.The inverse statement assumes the opposite of each of the original statements and is notated ∼p→∼q (if not p, then not q).The contrapositive statement is a combination of the previous two. The positions of p and q of the original statement are switched, and then the opposite of each is considered: ∼q→∼p (if not q, then not p).
So, from the above we can clearly see that the both the statement 1 and statement are not start with "if" and "then".
Therefore, their relationship cannot be determined.
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Determine the next three terms in the following sequence:
-1, 1/2, -1/4, 1/8, __, __, __,….
A. 1/12, 1/24, 1/48
B. 1/16, 1/32, 1/64
C. -1/16, 1/32, -1/64
D. -1/12, 1/24, -1/48
The next three terms in the sequence are -1/16, 1/32, -1/64
The correct option is option C)
What is a sequence?
A sequence is an set of values separated by commas Referring to a generalized rule. They have a relation among them. One of the common sequences are arithmetic progression
We are given a sequence of -1, 1/2, -1/4, 1/8,
We have to describe the next three terms of the sequence
If we notice closely the given sequence is an geometric sequence
Hence they have a common factor known as common ratio
in it we divide a term by its previous term
Hence
Ratio= (1/2)/-1
Ratio = -1/2
Now to find the next terms we multiply this with the last term we get
1/8*-1/2= -1/16
Now Hence the next three terms are -1/16, 1/32, -1/64
The correct option is option c)
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a.) find the test statistic
b.) what is the p-value
c.)what is the conclusion about the null hypothesis
d.) what is the final conclusion?
a) The test statistic is: t = 1.85.
b) The p-value is: 0.0648.
c) The null hypothesis is not rejected.
d) There is not sufficient evidence to conclude that the population mean is different of 4.
What is the test statistic?The standard deviation is known only for the sample, hence the t-distribution is obtain the test statistic.
The test statistic of the t-distribution is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the variables of the equation are given as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the hypotheses.s is the standard deviation of the sample.n is the sample size.For this problem, the values of these parameters are as follows:
[tex]\overline{x} = 4.32, \mu = 4, s = 4.24, n = 600[/tex]
Hence the test statistic is obtained as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{4.32 - 4}{\frac{4.24}{\sqrt{600}}}[/tex]
t = 1.85.
P-value and conclusionThe p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, with 600 - 1 = 599 df and t = 1.85, hence it is of 0.0648.
Since the p-value is greater than the significance level of 0.01, it is found that the conclusion regarding the null hypothesis is that it is not rejected, meaning that the sample does not give sufficient evidence to conclude that the population mean is different of 4.
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The sum of two numbers is 19/24 and their difference is 11/24, what are the two numbers?
The value of the the two numbers are 5/8and 1/6
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.
They are called simultaneous equations because the equations are solved at the same time.
if the first number is x and second number is y then
x+y= 19/24 equation 1
x-y= 11/24 equation 2
using elimination method, subtract equation 1 from 2
x-x+y-(-y)=19/24-11/24
2y= 8/24
2y=1/3
divide both side by 2
y= 1/3×1/2= 1/6
substitute 1/6 for y in equation 2
x+1/6=19/24
x= 19/24-1/6
x= 15/24
x= 5/8
Therefore the value of the two numbers is 5/8 and 1/6
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Help pls I will give brainliest!!
Answer:
C. -16
Step-by-step explanation:
Hope this helps you! :))
16
Step-by-step explanation:
the answer is c
just took a test and I got it right
Laura and Kirk are comparing how much they have been running. Laura has already
run 36 miles and Kirk has run 64. Laura begins running 21 miles per week and Kirk runs 17 miles
per week. How many additional weeks, w, will it take for their total distance run to be equal?
The additional weeks, w, will it take for their total distance run to be equal is 7 weeks.
How to calculate the number of weeks?From the information, Laura has already
run 36 miles and begins running 21 miles per week. This will be 36 + 21w.
Kirk has run 64 miles and runs 17 miles per week. This will be 64 + 17w
where w = number of weeks
This will be equated as:
36 + 21w = 64 + 17w
Collect like terms
21w - 17w = 64 - 36
4w = 28
Divide
w = 28/4
w = 7
It'll take 7 weeks.
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Lee Holmes deposited $17,000 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $42,000 at 9% interest compounded semiannually.
At the end of 6 years, what is the balance in Lee’s account? (Use the Table provided.)
The balance in Lee's account at the end of 6 years is $384,830.53.
What is the balance?The first step is to determine the future value of the initial amount deposited in the savings account.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate = 9% / 2 = 4.50%m = number of compoundingN = number of yearsBalance at the end of 3 years: $17,000 x (1.045)^(3 x2) = $22,138.42
The total value of the account after $42,000 is deposited is:
$42,000 + $22,138.42 = $64,138.42
The future value of $64,138.42 at the end of 6 years is:
Balance at the end of 6 years: $64,138.42 x (1.045)^(3 x2) = $384,830.53
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Find the value of x in the equation
4^x+16^x= 272
Answer:
x = 2
Step-by-step explanation:
(x2 + 3x –9) ÷ (x – 2).
Answer:
Step-by-step explanation:
15. Rachel Teeter has a monthly budget of $3000. She plans
to spend 34% for rent and utilities, 23% for food, 5% for
entertainment, 25% to pay off debt, and the remainder
will go into a savings account.
(a) What percent of the total budget will go into a savings
account?
Answer: 17%
Step-by-step explanation:
If you add up 34%, 23%, 5%, & 25% that would equal 83%, if you subtract the 83% from 100%, you would get 17%.The 17% is equivalent to 510. So Rachel Teeter will have $510 in her savings account.
f(x) = 2x^4-8x²+5x-7
x=3
[tex]{ \pink{ \boxed{ \purple{ \sf{f(3) = 98}}}}}[/tex]
Step-by-step explanation:
[tex]{ \blue{ \tt{f(x) = 2 {x}^{4} - 8 {x}^{2} + 5x - 7}}}[/tex]
[tex]{ \blue{ \tt{f(3) = 2( {3})^{4} - 8( {3})^{2} + 5(3) - 7}}}[/tex]
[tex]{ \blue{ \tt{f(3) = 2(81) - 8(9) + 15 - 7}}}[/tex]
[tex]{ \blue{ \tt{f(3) = 162 - 72 + 8}}}[/tex]
[tex]{ \blue{ \tt{f(3) = 162 - 64}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{f(3) = 98}}}}}[/tex]
WILL GIVE BROANLYEST 80 POINTS!!!!!!! What is the volume of a rectangular prism with a length of twenty-two and one-half feet, a width of 12 feet, and a height of 13 feet?
7,800 ft3
3,510 ft3
1,755 ft3
five hundred sixty-two and one-half ft3
Answer:7,800
Step-by-step explanation:
Answer:
Option B (3,510ft) would be correct.
Step-by-step explanation:
The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases. It has 6 faces (all are rectangular),12 sides, and 8 vertices. As the rectangular prism is a three-dimensional shape (3D shape), the unit that is used to express the volume of the rectangular prism is cm3, m3 and so on. In mathematics, any polyhedron, having all such characteristics can be referred to as a Cuboid.
y=2/3x-18 rate of change
The rate of change of the equation, y = 2/3x - 18, is: 2/3.
How to Determine the Rate of Change of a Linear Equation?The rate of change of a linear equation that is expressed in slope-intercept form as y = mx + b is represented by the value of m in the equation. It is also referred to as the slope of the equation.
For example, if we are given the equation, y = 4x + 5, the value of m is 4. This implies that the rate of change, which is the slope, is equal to 4.
In the same vein, we are given the equation, y = 2/3x - 18.
The value of m, which is the slope or rate of change in the equation y = 2/3x - 18 is equal to 2/3.
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bill wrote all the numbers from 1 to 1000. how many digits did he write down?
Answer:
2890 digits--------------------------
One - digit numbers1 to 9 ⇒ 9 numbersTwo - digit numbers10 to 99 ⇒ 100 - 10 = 90Three - digit numbers100 to 999 ⇒ 1000 - 100 = 900Four - digit number 1000 ⇒ 1Number of digits1*9 + 2*90 + 3*900 + 1 = 2890When driving mountain roads, road signs often indicate the steepness of the road as a % grade which represents the angle of elevation as the road rises. Imagine your job is to collect or measure the data that is needed to determine the % grade of mountain roads in a certain region of the U.S. Which of these quantities is needed for you to be able to use arcsine to calculate the % grade? Select all that apply.
a) The length of a section of the road
b) The angle of depression
c) The horizontal distance travelled
d) The change in elevation along a section of road
The quantity that is needed for you to be able to use arcsine to calculate the percentage grade is D. The change in elevation along a section of road
What is an elevation?A geographic location's elevation is its height above or below a set reference point, most typically a reference geoid, which is a mathematical model of the Earth's sea level as an equipotential gravitational surface.
Elevation is described as the height above the ground or other surface, as well as a location or position of elevation. A plane flying 36,000 feet above the ground is an illustration of elevation. A pope being elevated to the position of saint is an example of elevation.
When driving on mountain roads, road signs frequently reflect the route's steepness as a percentage grade, which represents the angle of elevation as the road increases. In this case, the correct option is D.
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Elizabeth and Herman are collecting aluminum cana for a frundraiser at their school. Elizabeth was able to collect 50 cans each day from Monday to Friday, Herman was able to collect double that amount each day except Friday, when he collected none. Each can is worth 2 cents. What are the quantities in this situation?
The total cans collected by both Elizabeth and Herman is 650 and the total amount of money realized is 1300 cents.
What is rate?A rate is a ratio in which the two terms being compared have different unit's.For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.
The aluminum cans collected by Elizabeth from Monday to Fridays is 50× 5days = 250 cans
Herman collected double from Monday to Thursday and collected non on Friday, therefore the total cans collected by Herman = 50×2× 4 days= 400cans
the total cans collected = 250+ 400 cans = 650cans
therefore the total money realized since 1 can is with 2 cent is 650× 2= 1300cents
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Everyone at Colin's school wore either brown or red for school spirit day. 126 out of the 600 students at the school wore brown. What percentage of the students wore brown?
Write your answer using a percent sign (%).
Answer:
21%
Step-by-step explanation:
126 out of 600=126/600
=0.21 *100 for
21%
Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a
brief evaluation of your work.
Activity
In the first Lesson Activity, you derived an equation to model a car wash. The equation is y = 5x - 75. In this activity, you will graph this equation.
Question 1
Is it possible to graph the line that represents this equation by using two points found in the previous Lesson Activity, (15, 0) and (0, -75)? Explain
your answer.
Yes, the graph goes through those two points.
What is Graph?
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Explanation for the answer:
The equation can be graphed by plotting the two given points and drawing a line through them. Such a graph is shown in the attachment.
You can graph a line for any linear equation from any two points that fit the equation. So you can use the points (0, -75) and (15, 0) to graph the line representing the situation.
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Sara sold a coin for $3, and its value increases by 2% each year after it is sold. Find the value of the coin in 8 years. Then write an exponential growth
function for this problem. After that, graph the function and state the domain and range. Finally, state what the y-intercept represents.
By using the concept of growth, it can be calculated that
Value of coin in 8 years is $3.52
[tex]3(\frac{51}{50})^x[/tex] is the required exponential function
Domain of the function is all positive real number
Range is [tex](0, \infty)[/tex]
y- intercept is 3
This means initial value of the coin is $3
What is growth?
Growth is the exponential increase in the value of the product at a certain rate over a certain period of time
Here, concept of growth has been used
Present value of the coin = $3
Rate = 2%
Time = 8 years
Future value =
[tex]3(1 + \frac{2}{100})^8\\\\3(1 + \frac{1}{50})^8 \\\\3(\frac{51}{50})^8[/tex]
= $3.52
If the time is x years, the given exponential function is
y =
[tex]3(1 + \frac{1}{50})^x\\\\3(\frac{51}{50})^x[/tex]
This is the required exponential function.
Since x represents time here, then x has to be positive
Domain of the function is all positive real number
Now
As [tex]x\rightarrow \infty[/tex], [tex]f(x) \rightarrow \infty[/tex]
As [tex]x\rightarrow -\infty[/tex], [tex]f(x) \rightarrow 0[/tex]
Range is [tex](0, \infty)[/tex]
For y- intercept, x = 0
Putting x = 0, we get y = 3
y- intercept is 3
This means initial value of the coin is $3
The graph of the function has been attached here
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A rectangle has an area of 14y³ - 63y.
a. What are expressions for the length and width where one dimension is
the GCF?
pls help.
The length and breadth expressions where one dimension is the GCF are; 7y and (2y²-5).
Area of a Rectangle
Given that a rectangle is a two-dimensional shape with one of the dimensions being the GCF, as specified in the question;
Consequently, the length and breadth expressions are 7y and (2y²-5) respectively.
Additionally, the rectangle's area when y=2 is; 14(2³) - 35(2) = 52.
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A pack of cards is shuffled and a card is chosen at random.
What is the probability of getting a black card?
Answer:
[tex]\dfrac{1}{2}[/tex]
Step-by-step explanation:
Probability:Number of cards = 52
Number of black cards = 13 (club) + 13 (spade)
= 26
[tex]\sf P(\text{getting a black card})=\dfrac{26}{52}[/tex]
[tex]\sf =\dfrac{1}{2}[/tex]
find quotient of 5 divided by 3/10
The quotient of 5 divided by 3/10 is equal to 50/3
How to divide by a fraction?When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.
So, if we want to divide A by the fraction (b/c), then we can write:
A÷(b/c)
That will be equal to A*(c/b), so:
A÷(b/c) = A*(c/b)
Here we want to divide 5 by 3/10, then we need to solve:
5÷(3/10)
Using the above rule we will get:
5÷(3/10) = 5*(10/3) = 50/3
That is the quotient.
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PLEASE HELP ASAP!! WILL GIVE BRAINLIEST
A regular polygon has 12 sides. If one of its angles measures (8h − 30)°, what is the value of h?
h = 10.75
h = 18.75
h = 20.25
h = 22.5
Answer: h = 22.5
Step-by-step explanation:
Total angle area of a 12 sided polygon is 1800
1. One angle would be 1800/12= 150
8h - 30 = 1502. Add 30 one each side to cancel out and only leave 8h.
8h = 1803. To get rid of the 8 we divide the the other side by 8.
h = 22.5The answer is 22.5
Answer: D 22.5 i got it right on the exam
Step-by-step explanation:
The expression 43πr3 represents the volume of a sphere, with radius r. Why is this expression a monomial?
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
It is the product of a number, represented by Response area, and a variable with a whole number exponent, represented by Response area.
Question 2
What is the degree of the monomial?
The degree is
.
Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
WE have been given an expression as 43πr³ represents the volume of a sphere, with radius r.
Terms can be added or subtracted to make a polynomial. They are composed of variables and constants all in multiplication.
So we know that if there is one term, then the polynomial will be called monomial.
Therefore, this expression is a monomial which have inly one term as 43πr³ .
Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.
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125 square foot to the nearest integer
When using re-grouping to solve 25 x 45, what are the four problems that would be calculated to find the final answer?
O20 x 40; 20 x 5; 40 x 5
O20 x 40; 5 x 40; 20 x 5; 5 x 5
20 x 40; 5 x 20; 20 x 5; 5 x 5
O 20 x 20; 40 x 40; 20 x 5; 5 x 5
HELP PLSSS☹️☹️☹️☹️☹️
The problem that would be calculated to find the final answer is 2) 20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125
Given,
When using re-grouping to solve 25 x 45, we have to find the problems that would be calculated to find the final answer;
Here,
25 × 45 = 1125
Now,
This is simply multiplicity;
1. 20 x 40: 20 x 5: 40 x 5
800 ; 100 ; 200
1100
This is not the problem.
2. 20 x 40; 5 x 40; 20 x 5 ; 5 x 5
800 ; 200 ; 100 ; 25
1125
This is the problem
3. 20 x 40 ; 5 x 20 ; 20 x 5 ; 5 x 5
800 ; 100 ; 100 ; 25
1025
This is not the problem
4. 20 x 20 ; 40 x 40 ; 20 x 5 ; 5 x 5
400 ; 1600 ; 100 ; 25
2125
This is not the problem
Therefore,
The problem that would be calculated to find the final answer is 2) 20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125
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PLEASE HELP!!!! I WILL GIVE YOU BRAINLIST!! PLEASE ASAP :)
Which graph shows the image of ΔABC after a rotation about the origin?
Answer:
D.
Step-by-step explanation:
just click the rotate button until it matches one of the answers
For the functions f(x)=2x4+2x3−x2+2x+3 and g(x)=x+1 find (fg)(x) and (fg)(−4)
The value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.
What is polynomial?A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
Given function is f(x) = 2x⁴ + 2x³− x²+ 2x + 3
The value of the function is calculated as,
f(x) = 2x⁴ + 2x³− x²+ 2x + 3
(fg)(x) = (2x⁴ + 2x³− x²+ 2x + 3)(x+1)
(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)
The value of (fg)(x) is calculated as,
(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)
(fg)(-4) = (2(-4)⁵ + 2(-4)⁴ + (-4)³ + (-4)² +5x-4 +3)
(fg)(-4) = -2048 +1024-64+16-20+3
(fg)(-4) = -1089
Therefore, the value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.
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What is the answers please
The answer of the given multiplication is 19.2, 1.7, 15.93 and 0.0512 respectively.
To find the answer, we will simply multiply the given numbers.
i) 3.2 × 6 = 19.2
ii) 8.5 × 0.2 = 1.7
iii) 2.7 × 5.9 = 15.93
iv) 0.32 × 0.16 = 0.0512
Hence, the answers is 19.2, 1.7, 15.93 and 0.0512 respectively.
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Question 1-3
Tim and Jessica plan to rent a camper van for a vacation. The van costs $183. 00 per day. The rental includes 120 miles for free and then charges $0. 39 per mile.
Part A
Select the equation that models the cost of the van rental. V in terms of miles traveled m
V= 183 + 0.39(m
120)
O V = 0.39m + (183
- 120)
0 m = 183 + 0.39(V - 120)
0 m = 0.039V + (183 - 120)
Tim and Jessica's vacation budget is to spend a total of $598. 74 for the rental van. Use the equation to determine the number of miles that Tim and Jessica can travel roundtrip on
vacation.
Destination
Boston, MA
Asheville. NC
Nashville. TN
Washington. D.C.
Miles from Rental Company to Destination
1186 miles
593 miles
687 miles
846 miles
Select the destination that Tim and Jessica can go on vacation based on the budget.
O Boston, MA
O
Asheville, NC
Nashville, TN
O Washington, D.C.
The equation that models the cost of the van rental is V = $183 + (m - 120)0.39. (first option)
The number of miles that Tim and Jessica can travel roundtrip on vacation is Ashville MC (second option)
How many miles can they travel?The equation that represents the total cost of renting the camper van is a linear equation. A linear equation is an equation that has single variable that is raised to the power of one.
The general form of a linear equation is: y = mx + b
Where:
m = slope b = interceptThe form of the linear equation is:
total cost = cost of renting the van + [(total miles driven - 120) x cost per mile)
V = $183 + (m - 120) x 0.39
V = $183 + (m - 120)0.39
Total miles that can be driven if they have to spend $598.74
$598.74 = $183 + (m - 120)0.39
$598.74 = $183 + 0.39m - 46.80
$598.74 = $136.20 + 0.39m
$598.74 - $136.20 = 0.39m
$462.54 = 0.39m
m = $462.54 /0.39
m = 1186
Distance Tim and Jessica can travel from the rental company to the destination = 1186 / 2 = 593 miles
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rewrite 11/12 in two different ways