Given:
Betty and Theresa together complete a job in 20 hours.
Betty alone does a work in 60 hours.
The aim is to find the time Theresa will take to complete the job alone.
Therefore,
Betty and Theresa's 1 day work:
[tex]=\frac{1}{20}[/tex]Betty's 1 day work when he works alone:
[tex]=\frac{1}{60}[/tex]Now, Theresa's 1 day work when he works alone is given by:
[tex]\begin{gathered} =\frac{1}{20}-\frac{1}{60} \\ =\frac{3-1}{60} \\ =\frac{2}{60} \\ =\frac{1}{30} \end{gathered}[/tex]Hence, Theresa can do the job in 30 hours working alone.
Manny opened a savings account 7 years ago the account earns 9%interest compounded monthly if the current balance is 400.00 how much did he deposit initially
We have the following:
The formula for compound interest is as follows
[tex]\begin{gathered} A=P(1+r)^t \\ \end{gathered}[/tex]A is amount (current balance 400), P is the principal ( deposit initially), r is the rate (0.07) and is the time ( 7 years)
replacing:
[tex]\begin{gathered} 400=P(1+0.07)^{7^{}} \\ P=\frac{400}{(1.07)^7} \\ P=249.09 \end{gathered}[/tex]Which means that the initial deposit was $ 249.09
Could I please get help with finding the correct statements and reasonings. I think I messed up line number four because it keeps saying the line is incorrect and that I can not validate it l but
Answer:
Step-by-step explanation:
[tex]undefined[/tex]Use the graph shown to the right to find each of the following
The x intercept is the value of x at the point where the curve touches the x axis of the graph. Looking at the graph,
x intercept = - 1
It is written as (- 1, 0)
The zeros of the quadratic function is the same as the x intercept. Since the curve touches the x axis at only x = - 1, the zeros would be
x = - 1 twice
In the circle below, if the measure of arc ACB = 260 °, find the measure of < B.
Given:
There is a figure given in the question as below
Required:
If
[tex]arcACB=260\degree[/tex]than find the value of angle B
Explanation:
Value of arcADB is
[tex]arcADB=360\degree-arcACB=360\degree-260\degree=100\degree[/tex]Now to find the angle B
[tex]\angle B=\frac{1}{2}arcADB=\frac{1}{2}*100=50\degree[/tex]Final answer:
a
In a survey of 200 college students it is found that:61 like cooking32 like reading73 like video games19 like both cooking and reading23 like cooking and video games92 like reading or video games6 like all 3 hobbiesa. How many do not like any of these hobbiesb how many like reading onlyc how many like reading and video gamesd how many do not like cooking or video games
Given:
The number of total students = 200
The number of students like cooking = 61
The number of students who like reading = 32
The number of students who like both cooking and reading= 19
The number of students who like video games = 73
The number of students who like cooking and video games= 23
The number of students who like reading and video games = 92
The number of students who like all 3 hobbies = 6
Required:
(a)
7. Julie has $250 to plan a party. There is a one-time fee of $175 to reserve a room. It also cost $1.25 perperson for food and drinks. What is the maximum number of people that can come to the dance?
Julie has $250 to plan the party.
The room costs $175 to reserve plus $1.25 per person for food and drinks.
Let "x" represent the number of people she can invite, you can express the total cost for the party as follows:
[tex]175+1.25x\leq250[/tex]From this expression, we can determine the number of people she can invite, without exceeding the $250 budget.
The first step is to pass 175 to the right side of the expression by applying the opposite operation "-175" to both sides of it:
[tex]\begin{gathered} 175-175+1.25x\leq250-175 \\ 1.25x\leq75 \end{gathered}[/tex]Next, divide both sides of the equation by 1.25 to reach the value of x:
[tex]\begin{gathered} \frac{1.25x}{1.25}\leq\frac{75}{1.25} \\ x\leq60 \end{gathered}[/tex]She can invite up to 60 people to the party
While munching on some skittles, Bobby the Vampire lost a tooth that just so happened to be one of his fangs. He measured it to be 27 centimeters long. How long was his tooth in inches?
Answer: 10.6299
Step-by-step explanation:
There are 0.3937 inches in a cm., So, the length of the tooth in inches is [tex]27(0.3937)=10.6299 \text{ in }[/tex]
what is the answer to 850x+40(x)
ANSWER
854x
EXPLANATION
We have that:
850x + 40(x)
First, expand the bracket:
850x + 40x
Because the two terms are of the same kind (terms of x) we can add them up:
850x + 4x = 854x
That is the answer.
Use inductive reasoning to find a pattern then make a reasonable conjecture for the next three items in the pattern p g q h r I
Consider the first, third, and fifth terms of the sequence: p,q,r; these are consecutive letters starting with p.
Similarly, as for the second, fourth, and sixth terms: g,h, i; these are consecutive letters starting with g.
Thus, the seventh term has to be the letter that follows r; this is, s.
Analogously, the eighth and ninth terms are
[tex]\begin{gathered} \text{ eighth}\to\text{letter that follows i}\to j \\ \text{ ninth}\to\text{ letter that follows s}\to t \end{gathered}[/tex]Thus, the missing terms are: s, j, and t.
Two ships left a port at the same time. Onetravelled due north and the other due eastat average speeds of 25.5 km/h and 20.8 km/h,respectively. Find their distance apart
Given:
Two ships left a port at the same time.
One travelled due north at an average speed of 25.5 km/h
And the other ship was due east at average speeds of 20.8 km/h
We will find their distance apart using the Pythagorean theorem.
The distance = Speed * Time
Let the time = t
So, the distance of the first ship = 25.5t
And the distance of the second ship = 20.8t
So, the distance between the ships (d) will be as follows:
[tex]\begin{gathered} d^2=(25.5t)^2+(20.8t)^2 \\ d^2=1082.89t^2 \\ \\ d=\sqrt{1082.89t^2} \\ d=32.907t \end{gathered}[/tex]So, the answer will be:
The distance in terms of time = 32.907t
We will find the distance when t = hours
So, distance = 164.54 km
Use the trapezoidal approximation to estimate he distance the turtle traveled from 0 to 10 seconds.
we have that
The trapezoidal approximation is equal to
[tex]A=\frac{1}{2}\cdot\lbrack f(a)+f(b)\lbrack\cdot(b-a)[/tex]where
a=0
b=10
f(a)=f(0)=0.05
f(b)=f(10)=0.043
substitute given values
[tex]\begin{gathered} A=\frac{1}{2}\cdot\lbrack0.05+0.043\lbrack\cdot(10-0) \\ A=0.465\text{ m} \end{gathered}[/tex]therefore
the answer is 0.465 metersWhat is the slope between (2,-1 ) and ( 5,4 )
the slope will be 5/3 because:
[tex]\frac{4-(-1)}{5-2}=\frac{5}{3}[/tex]solve the equation x 1.)132.)13/33.) 104.) none of these choices
Answer:
2. 13/3
Step-by-step explanation:
x will be equal to 13/3.
Given,
5^(2x - 1) = 5^(5x - 14)
We can see that base is the same for both the exponents on each side of the equation.
Now, on using the Logarithm on both sides with base 5, we can see that the base on both sides of the equation cancels out with the log (base 5) function.
And new equation becomes:
(2x - 1) = (5x - 14)
This derives us to another conclusion that if the base of an exponent is equal then,
the powers must be equal too.
(2x - 1) = (5x - 14)
=> 5x - 2x = -1 + 14
=> 3x = 13
which gives us,
=> x = 13/3.
Therefore x = 13/3.
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15=g/7 what does g equal to
Answer:
g = 105
Explanation:
We want to find the value of g if
[tex]15=\frac{g}{7}[/tex]We multiply both sides of the equation by 7
[tex]\begin{gathered} 15\times7=\frac{g}{7}\times7 \\ \\ 105=g \end{gathered}[/tex]Therefore, the value of g is 105
Answer:
[tex]15=g/7[/tex]
We can get the value of g by multiplying the denominator, which in this case is 7.
So,
[tex]g = 15 x 7\\ g=105[/tex]
how many seconds does it take until the ball hits the ground ?
Given:
The quadratic model of the ball is given as:
[tex]h(t)=-16t^2+104t+56[/tex]Required:
Find the time when it takes to hit the ground.
Explanation:
When the ball hits the ground then h(t)=0.
[tex]\begin{gathered} -16t^2+104t+56=0 \\ -8(2t^2-13t-7)=0 \\ 2t^2-13t-7=0 \end{gathered}[/tex]Solve the quadratic equation by using the middle term splitting method.
[tex]\begin{gathered} 2t^2-14t+t-7=0 \\ 2t(t-7)+1(t-7)=0 \\ (t-7)(2t+1)=0 \\ t=7,-\frac{1}{2} \end{gathered}[/tex]Since time can not be negative.
So t = 7 sec
Final Answer:
The ball will take 7 sec to hits the ground.
Write the number 0.2 in the form a over b using integers to show that it is a rational number
Hello! Let's solve this exercise:
We have some ways to show it, look:
[tex]\begin{gathered} \frac{a}{b}=0.2 \\ \\ \frac{1}{5}=0.2 \\ \\ \frac{2}{10}=0.2 \end{gathered}[/tex]So, as it can be written as a fraction, is a rational number.
1. Which expression is equivalent to 2 x (5 x 4)?a. 2+ (5 x 4)b. (2 x 5) x 4c. (2 x 5) x 4d. (5 x 4) x (2 X4)
We are given the following expression
[tex]2\times(5\times4)[/tex]Recall the associative property of multiplication
[tex]a\times(b\times c)=(a\times b)\times c[/tex]The associative property of multiplication says that when you multiply numbers, you can group the numbers in any order and still you will get the same result.
So, if we apply this property to the given expression then it becomes
[tex]2\times(5\times4)=(2\times5)\times4[/tex]Therefore, the following expression is equivalent to the given expression.
[tex](2\times5)\times4[/tex]Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
Answer: y=80+2x
Step-by-step explanation:
In y=mx+b format the answer is y=80+2x
(f o g)(x) = x(g o f)(x) = xwrite both domains in interval notation
the fact that both functions are polynomial of degree 1 we get that the domain and range of both functions are the real numbers. In intervalo notation this is:
[tex]\begin{gathered} \text{domain:}(-\infty,\infty) \\ \text{range:}(-\infty,\infty) \end{gathered}[/tex]The long-distance calls made by South Africans are normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes for 1500 south Africans what is the expected number of callers whose calls last less than 15 minutes?
The question provides the following parameters:
[tex]\begin{gathered} \mu=16.3 \\ \sigma=4.2 \end{gathered}[/tex]For 15 minutes, the z-score is calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]At x = 15:
[tex]z=\frac{15-16.3}{4.2}=-0.3[/tex]The probability is calculated using the formula:
[tex]P(X<15)=Pr(z<-0.3)=Pr(z<0)-Pr(0From tables, we have:[tex]\begin{gathered} Pr(z<0)=0.5 \\ Pr(0Therefore, the probability is given to be:[tex]\begin{gathered} P(X<15)=0.5-0.1179 \\ P(X<15)=0.38 \end{gathered}[/tex]The expected number of callers will be calculated using the formula:
[tex]\begin{gathered} E=xP(x) \\ At\text{ }x=1500 \\ E=1500\times0.38 \\ E=570 \end{gathered}[/tex]Therefore, the expected number of callers whose calls last less than 15 minutes is 570 callers.
polynomials - diving polynomialssimplify the following expression with divisionbare minimum of steps
I think I’m off to a good start but I’m still confused
The radius is given 3.5 ft and height is given 14 ft.
ExplanationTo find the surface area of cylinder,
Use the formula.
[tex]S=2\pi rh+2\pi r^2[/tex]Substitute the values.
[tex]\begin{gathered} S=2\pi r(h+r) \\ S=2\times3.14\times3.5(14+3.5) \\ S=384.65ft^2 \end{gathered}[/tex]The volume of cylinder is determined as
[tex]V=\pi r^2h[/tex]Substitute the values
[tex]\begin{gathered} V=3.14\times3.5^2\times14 \\ V=538.51ft^3 \end{gathered}[/tex]AnswerThe surface area of cylinder is 384.65 sq.ft.
The volume of cylinder is 538.51 cubic feet.
the length of a screwdriver is 0.75 cm is how many screws can be placed to the end to make a road that's 18 cm long show yours
Length of screwdriver = 0.75
Length of road = 18cm
Number of screws that can be placed on a road
[tex]\begin{gathered} =\text{ }\frac{18}{0.75} \\ =\text{ 24} \end{gathered}[/tex]3 4. Diego estimates that there will need to be 3 pizzas for every 7 kids at his party. Select all the statements that express this ratio. (Lesson 2-1) (A.) The ratio of kids to pizzas is 7 : 3. B.) The ratio of pizzas to kids is 3 to 7. The ratio of kids to pizzas is 3: 7. (D. The ratio of pizzas to kids is 7 to 3. E. For every 7 kids, there need to be 3 pizzas.
The statements in (A), (B), (E) are correct and satisfy the conditions in question.
What is ratio and proportion?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. Because b is not equal to 0, the ratio establishes the link between two quantities such as a:b.
Given, for every 7 kids, pizzas needed = 3 --(iii)
Therefore, for every 1 kid, pizza needed = (3/7)
Thus, for every x kids, pizza needed = (3/7)x
Again, ratio of pizzas to kids is = 3:7 --(i)
Also, the ratio of kids to pizza is = 7:3 --(ii)
From (A), using (ii), the statement in (A) is correct.
From (B), using (ii), the statement in (B) is correct.
From (C), using (i), the statement in (C) is incorrect.
From (D), using (i), the statement in (D) is incorrect.
From (E), using (iii), the statement in (E) is correct.
Thus, the statements in (A), (B), (E) are correct and satisfy the conditions in question.
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The graph shows the function f(x) = |x – h| + k. What is the value of h?
h = –3.5
h = –1.5
h = 1.5
h = 3.5
f(x)=x^6+10x^4 - 11x^2
You can notice that the given function is symmetric respect to the y-axis.
It means that the value of the function for both x and -x is the same:
[tex]f(-x)=f(x)[/tex]This is the characteristic of a even function.
Hence, the answer is B
Help with number one a and b is both parts of number one
Solving the operation_
We are given two figures that represent a garden. We are asked to determine its areas.
The shape of figure A is a rectangle of 9 ft by 12 ft. The area of a rectangle is the product of its dimensions therefore, we have:
[tex]A_A=\left(9ft\right)\left(12ft\right)[/tex]Solving the operations:
[tex]A_A=108ft^2[/tex]The shape of figure B is a circle of radius 5ft. The area of a circle is:
[tex]A_B=\pi r^2[/tex]Where "r" is the radius. Substituting we get:
[tex]A_B=\pi\left(5ft\right)^2[/tex][tex]A_B=25\pi ft^2[/tex]In decimal notation, the area is:
[tex]A_B=78.54ft^2[/tex]From the given information. Write the recursive and explicit functions for each geometric sequence. Please use these terms. recursive f(1) = first term, f(n) = pattern*f(n-1). what is the 1st term and pattern? explicit is y = pattern^x * 0 term. work backwards to find 0 term
We know that a geometric sequence is given by:
[tex]f(n)=f(1)r^{n-1}[/tex]where r is the common ratio of the sequence.
For this sequence we have that the common ratio is r=2, this comes from the fact that in the first day we have 6 dots, for the second day we have twelve and for the third day we have 24. We also notice that the first term is:
[tex]f(1)=8[/tex]Therefore the sequence is given by:
[tex]f(n)=8(2)^{n-1}[/tex]Now, to find the zeoth term we plug n=0 in the sequence above, therefore the zeroth term is:
[tex]\begin{gathered} f(0)=8(2)^{0-1} \\ f(0)=8(2)^{-1} \\ f(0)=4 \end{gathered}[/tex]16. Solve for "x".
a. 6
b. 100
c. 36
Answer:
A. 6
Step-by-step explanation:
Using the Pythagorean theorem which states that: Hypotenus² = Opposite² + Adjacent²
Where: hypotenus = 10, opposite = x, adjacent = 8
So:
[tex] {10}^{2} = {x}^{2} + {8}^{2} [/tex]
Solving for x
[tex]100 = {x}^{2} + 64[/tex]
Collect like terms to make x the subject of formula
[tex]100 - 64 = {x}^{2} →36 = {x}^{2} [/tex]
[tex]36 = {x}^{2} ⟹ {x}^{2} = 36[/tex]
square root both sides of the equation to find the value of x
[tex] \sqrt{ {x}^{2} } = \sqrt{36} →x = 6[/tex]
Therefore: Option A is correct
The probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, what is the probability that two or more of them will fail the test
If the probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, then the probability that two or more of them will fail the test is 0.41
The probability of failing a test = 0.115
Total number of people = 12
We have to find the probability that two or more of them will fail the test
We know the binomial distribution
P(X≥2) = 1 - P(X<2)
= 1 - P(X=0) - P(X=1)
P(X≥2)= 1 - [tex](12C_{0}) (0.115^0)(1-0.115)^{12}[/tex] - [tex](12C_{1}) (0.115^1)(1-0.115)^{11}[/tex]
= 0.41
Hence, if the probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, then the probability that two or more of them will fail the test is 0.41
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