Answer
x = 3
Explanation
The equation is given as
[tex]\frac{k+7}{x+1}=\frac{5}{2}[/tex]If k = 3, then we are asked to solve for x.
[tex]\begin{gathered} \frac{3+7}{x+1}=\frac{5}{2} \\ \frac{10}{x+1}=\frac{5}{2} \\ \text{Cross multiply} \\ 5(x+1)=2\times10 \\ 5x+5=20 \\ \text{Subtract 5 from both sides} \\ 5x+5-5=20-5 \\ 5x=15 \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{15}{5} \\ x=3 \end{gathered}[/tex]Hope this Helps!!!
Suppose a jar contains 10 red marbles and 23 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Round to at least 2 decimal places.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
red marbles = 10
blue marbles = 23
Step 02:
probability:
probability (event) = favorable outcomes / total outcomes
1. probability (red marble):
[tex]p=\frac{10}{23+10}=\frac{10}{33}=0.30303[/tex]2. probability (red marble):
[tex]p=\frac{9}{23+9}=\frac{9}{32}=0.28125[/tex]total probability:
[tex]p=0.30303*0.28125=0.0852=0.09[/tex]The answer is:
p = 0.09
a gardener planted flowers of different colors. 3/10 of the flowers are Yellow.3/4 of the remaining flowers are green.The rest of the flowers are purple.
3s+2t=-4-6s-10t=-7Value of s
Answer :
s = -3
Explanation :
Using method of substitution by expressing one equation to only one variable.
Equation 1 : 3s + 2t = -4
Equation 2 : -6s - 10t = -7
Express equation 1 as t in terms of s :
[tex]\begin{gathered} 3s+2t=-4 \\ 2t=-3s-4 \\ t=\frac{-3s-4}{2} \end{gathered}[/tex]Substitute t to the equation 2 :
[tex]\begin{gathered} -6s-10t=-7 \\ -6s-10(\frac{-3s-4}{2})=-7 \\ -6s-5(-3s-4)=-7 \\ -6s+15s+20=-7 \\ 9s=-7-20 \\ 9s=-27 \\ s=-\frac{27}{9}=-3 \end{gathered}[/tex]The answer is s = -3
2 poin #1 You start by adding $5 to your bank account, each week after that you will double what you are depositing. Week 1 you would deposit $10, week 2 $20 and so on. How much money would you be depositing on week 10?
the initial money deposit is 5 $ in the starting
Verona is solving the equation -3+4x=9. In order to isolate the variable term using the subtraction property of equality, which number should she subtract from both sides of the equation. A: -4B: -3C: 3D: 4
In order to solve the equation, we should do:
[tex]\begin{gathered} -3+4x=9 \\ -3+4x+3=9+3 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]Then, in the step to isolate the variable term (4x), we should add 3 to both sides of the equality (see step 2).
Answer: C: 3.
I need help finding the area of the pentagon please.
Given:
To Find:
The area of a given diagram
Formula:
[tex]\begin{gathered} \text{Area of a rectangle=l}\times w \\ \text{Area of a triangle=}\frac{1}{2}\times base\times height \end{gathered}[/tex]Explanation:
Area of a given diagram can be found by the sum of two shapes that is rectangle and triangle.
[tex]\begin{gathered} \text{Area}=Area\text{ of a rectangle+Area of a triangle} \\ =(8\times7)+(\frac{1}{2}\times7\times3) \\ =56+(\frac{21}{2}) \\ =56+10.5 \\ =66.5cm^2 \end{gathered}[/tex]Final Answer:
[tex]\text{Area}=66.5cm^2[/tex]Which equation represents a line which is parallel to the line x + 8y = 56?
Explanation
when two lines are parallel, their slopes are equal
if two lines with slope(m1) and slope(2) are parallel,then
[tex]m_{_1}=m_2[/tex]Step 1
convert the function into the form
[tex]\begin{gathered} y=\text{ mx+b } \\ \text{where m is the slope} \end{gathered}[/tex]then,
[tex]\begin{gathered} x+8y=56 \\ i)\text{ subtract x in both sides} \\ x+8y-x=56-x \\ 8y=56-x \\ divide\text{ both sides by 8} \\ \frac{8y}{8}=\frac{56}{8}-\frac{x}{8} \\ \\ y=-\frac{1}{8}x+7\rightarrow y=mx+b \end{gathered}[/tex]so, the slope of the function we are looking for is -1/8
Step 2
Mr.Jackson made a one time deposit of $57,000 into his retirement account when he was 25 years old. The account has an annual interest rate of 3.35%. If Mr.Jackson checks this retirement account when he is 72 years old. A. How much will he have earned in interest?B. What will be the total amount in his retirement account.
First we have to calculate how many yeas has pass from the date of the deposit and when he is 72 years old so:
[tex]72-25=47[/tex]So has pass 47 yeas, now we can calculate how much will he have earned in interest like this:
[tex]57000(1+0.035)^{47}=287125.19[/tex]so in interes will be the resto of this value minus the initial amound:
[tex]287125.19-57000=230125.19[/tex]In interest he earned 203,125.19 and the total amount is: 287,125.19
Simplify6(5x-2)-(3x-4)
ANSWER
27x - 8
EXPLANATION
We have the expression:
6(5x - 2) - (3x - 4)
First, we expand the bracket:
(6 * 5x) - (6 * 2) - 3x + 4
30x - 12 - 3x + 4
Collect like terms:
30x - 3x - 12 + 4
27x - 8
That is the answer.
Use the equation of the line of best fit to fill in the blanks below Give exact answers, not rounded approximations
Explanation:
The equation for the line of best fit is given as:
[tex]y=0.6x+19.85[/tex]Part A
Number of Hours Worked: 8.1
Observed Amount (from the table): 24.71
Predicted Amount:
[tex]\begin{gathered} y=0.6x+19.85 \\ =0.6(8.1)+19.85 \\ =24.71 \end{gathered}[/tex]Residual: The residual is the difference between the actual and predicted values.
[tex]\begin{gathered} \text{ Residual}=\text{ Actual Value-Predicted Value} \\ =24.71-24.71 \\ =0 \end{gathered}[/tex]Part B
Number of Hours Worked: 10.00
Observed Amount (from the table): 21.50
Predicted Amount:
[tex]\begin{gathered} y=0.6x+19.85 \\ =0.6(10)+19.85 \\ =25.85 \end{gathered}[/tex]Residual: The residual is the difference between the actual and predicted values.
[tex]\begin{gathered} \text{ Residual}=\text{ Actual Value-Predicted Value} \\ =21.50-25.85 \\ =-4.35 \end{gathered}[/tex]Answer:
The completed table is attached below:
the number of computers and students in a school is proportional and is shown in the table below
Given a table shows the number of computers and the number of students
We need to find the ratio between them:
So,
using the data of any row to find the ratio
So, the ratio of students to computers =
[tex]\frac{114}{19}=6[/tex]It can be written 6 or 6 : 1
Find f (-2).if f (x) = x²+ 2x- 6
Find f (-2).if f (x) = x²+ 2x- 6
Remember that
f(-2) is the vaue of f(x) when the value of x =-2
substitute
f (-2) = (-2)²+ 2(-2)- 6
f(-2)=4-4-6
f(-2)=-6Mrs. Kelly is making pizzas and she uses 20 slices of pepperoni on each pizza how many pepperoni slices will she need if she makes seven pizza
Given Mrs. Kelly uses 20 slices of pepperoni on each pizza.
If whe makes seven pizzas let the slices of pepperoni be x.
Then x is equal to
[tex]x=7\times20=140[/tex]16+2x=22 solve for x
16+2x=22 solve for x
step 1
subtract 16 both sides
2x=22-16
2x=6
step 2
Divide by 2 both sides
x=6/2
x=3
therefore
the ananswer is
x=31 Felipe surveyed students at his school. He found that 78 students own a cell phone and 57 of those students own an MP3 player. There are 13 students that do not own a cell phone, but own an MP3 player. Nine students do not own either device Construct a two-way table summarizing the MP3 Player No MP3 Player Total Cell Phone No Cell Phone Total 1 2 3 4 5
students that own a cell phone but don't own an MP3: 78 - 57 = 21
total number of student with no cell phone: 13 + 9 = 22
total number of student with a MP3 player: 57 + 13 = 70
total number of student without a MP3 player: 21 + 9 = 30
total number of students: 70 + 30 = 78 + 22 = 100
MP3 player no MP3 player Total
cell phone 57 21 78
no cell phone 13 9 22
Total 70 30 100
Solve /x-5/=3A. x=2, x=8B. x=-8, x=8C. x=-2, x=2D. x=-8, x=-2
According to the given data we have the following equation:
|x-5|=3
In order to solve the equation above we would make the following:
[tex]\mathrm{Apply\: absolute\: rule}\colon\quad \mathrm{If}\: |u|\: =\: a,\: a>0\: \mathrm{then}\: u\: =\: a\: \quad \mathrm{or}\quad \: u\: =\: -a[/tex]So, if x-5=-3. x=-3+5. x=2
Therefore the value of x would be 2
if x-5=3.x=3+5.x=8
Therefore the value of x would be 8.
Therefore, the combine solution would be:
x=2
x=8
the grocery store needs 50 cases of soda to complete a display. There are 27 cases available. How many more cases does the store need?
Given that
The grocery store has 27 cases and needs some more to complete the display.
And we have to find the remaining number of cases.
Explanation -
Let the number of cases required is x.
Now, the grocery store has 27 cases and it needs 50 cases to complete the display.
Then,
It means that the store requires a total of 50 cases.
And this situation can be written as
x + 27 = 50
x = 50 - 27
x = 23
So the cases required will be 23.
Final answer - Therefore the final answer is 23.perform the following operation(-4)(-19)(-2)
Explanation:
When solving a product, if the number of negative factors is even the result will be positive. If it's odd then the result will be negative.
In this case we have to multiply three negative numbers, which is an odd amount. Therefore the result is negative. We can solve the multiplication as if all the numbers were positive and then add the negative sign to the result:
[tex]-(4\times19\times2)=-((4\times19)\times2)=-(76\times2)=-152[/tex]Answer:
(-4)(-19)(-2) = -
Need an equation that makes a parabola from soccer ball over soccer dummy and into the garbage can
Answer:
The position of David Beckham is at (2,0) and the position of the garbage can is (38,0). Note that these two points would be the roots of the parabola we are going to draw.
Now since we have the roots, we can construct the equation of the parabola as
[tex]-a(x-2)(x-38)[/tex]where a is a constant.
We choose a = 0.05 and get
[tex]-0.05(x-2)(x-38)[/tex]Which is an equivalent expression of: 6 ( 3× + 5 ) - 11
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
6 ( 3x + 5 ) - 11
Step 02:
We must apply the algebraic rules.
6 ( 3x + 5 ) - 11
18x + 30 - 11
18x + 19
The answer is:
18x + 19
can you solve theis by the system of linear equations by elimination
To solve the system of equation using elimination, notice that the coefficient of the variable y appears with -3 in one equation and with 3 in the other. Since 3 and -3 are additive inverse numbers, then they will cancel out when added.
Then, add both equations: left hand side plus left hand side equals right hand side plus right hand side:
[tex]\begin{gathered} 2x-3y=9 \\ 5x+3y=12 \\ \Rightarrow2x-3y+5x+3y=9+12 \\ \Rightarrow2x+5x-3y+3y=21 \\ \Rightarrow7x=21 \\ \Rightarrow x=\frac{21}{7} \\ \Rightarrow x=3 \end{gathered}[/tex]Substitute back x=3 in one of the equations and solve for y:
[tex]\begin{gathered} 5x+3y=12 \\ \Rightarrow5(3)+3y=12 \\ \Rightarrow15+3y=12 \\ \Rightarrow3y=12-15 \\ \Rightarrow3y=-3 \\ \Rightarrow y=-\frac{3}{3} \\ \Rightarrow y=-1 \end{gathered}[/tex]Therefore, the solution to this system, is:
[tex]\begin{gathered} x=3 \\ y=-1 \end{gathered}[/tex]use the discriminant to find the nature of the solutions to the following quadratic equation3x^2 -2x-4=0Two different irrational number solutionsOne repeated irrational number solutiontwo different rational number solutionsOne repeated rational number solutiontwo imaginary number solution
The quadratic equation is
3x^2 - 2x - 4
using completing the square method
firstly, to solve a quadratic equation the coefficient x^2 must be 1
divide through by 3
3x^2/3 -2x/3 - 4/3 = 0
make the linear expression a perfect square
x^2 - 2x/3 = 4/3
make -2x/3 a perfect square
x^2 - 2x/3 x 1/ 2 = 4/3
x^2 - 2x/6 = 4/3
square -2x/6
x^2 -(2x/6)^2 = 4/3
add the perfect square to both sides
x^2 - (2x/6)^2 = 4/3 + (2/6)^2
(x - 2/6)^2 = 4/3 + 4/36
solve the left hand side of the equation
4/3 + 4/36
lcm is 36
4 * 12 + 4 *1 / 36
48 + 4 / 36
52/36
(x - 2/6)^2 = 52/36
find the squareroot of both sides
[tex]\begin{gathered} \text{x -2/6 }\pm\text{ }\sqrt[]{\frac{52}{36}_{}} \\ x\text{ = 2/6 }\pm\text{ }\frac{\sqrt[]{52}}{6} \\ \end{gathered}[/tex]square root of 52 is 7.211
x = 2 + 7.211 / 6 0r 2 - 7.211 / 6
x = 9.211 / 6 or -5.211/6
x = 1.53 or -0.8685
the answer is two different rational number solutions
The Floor Area of a Guest Room in the diagram is 12 x 8. If the room expanded to 40% increase, what are the new dimensions of the room?
First let's calculate the initial area, by multiplying the dimensions:
[tex]\begin{gathered} A=12\cdot8 \\ A=96 \end{gathered}[/tex]Now, let's increase this area by 40%, multiplying it by 1.4:
[tex]A=96\cdot1.4=134.4[/tex]Finally, to find the new dimensions, we just need to multiply them, knowing that they have the proportion of 12:8
[tex]\begin{gathered} x\cdot y=134.4 \\ \frac{x}{y}=\frac{12}{8}\to8x=12y\to x=\frac{12}{8}y \\ \\ (\frac{12}{8}y)\cdot y=134.4 \\ y^2=134.4\cdot\frac{8}{12} \\ y^2=89.6 \\ y=9.466 \\ \\ x=\frac{12}{8}y=\frac{12}{8}\cdot9.466=14.199 \end{gathered}[/tex]So the new dimensions are 14.199 and 9.466
A rectangle is twice as long as it is wide. If the length and width are both increased by 5 cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original rectangle to the nearest hundredth.
Considering the sides of the rectangle are:
w = width
l = lenght
Since it is twice as long as it is wide:
l = 2w
The area of a rectangle (A) is the product of the width and length.
Then,
A = lw
Knowing that: If the length and width are both increased by 5 cm, the resulting rectangle has an area of 50cm^2, then:
[tex]50=(l+5)*(w+5)[/tex]Substituting l by 2w:
[tex]50=(2w+5)*(w+5)[/tex]Solving the multiplications:
[tex]\begin{gathered} 50=2w*w+2w*5+5*w+5*5 \\ 50=2w^2+10w+5w+25 \\ 50=2w^2+15w+25 \end{gathered}[/tex]Subtracting 50 from both sides:
[tex]\begin{gathered} 50-50=2w^2+15w+25-50 \\ 2w^2+15w-25=0 \end{gathered}[/tex]To find w, use the quadratic formula.
For a quadratic equation ax² + bx + c = 0, the quadratic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In this question:
x = w
a = 2
b = 15
c = -25
Substituting the values:
[tex]\begin{gathered} w=\frac{-15\pm\sqrt{(-15)^2-4*2*(-25)}}{2*2} \\ w=\frac{-15\pm\sqrt{225+200}}{4} \\ w=\frac{-15\pm20.62}{4} \\ w_1=\frac{-15-20.62}{4}=\frac{-35.62}{4}=-8.90 \\ w_2=\frac{-15+20.62}{4}=\frac{5.62}{4}=1.40 \end{gathered}[/tex]Since the measure must be posite, width = 1.40 cm.
Also, l = 2w.
Then, l = 2*1.40
l = 2.80 cm.
Answer:
width = 1.40 cm
length = 2.80 cm.
I need help with this problem
The probability of an event is the chance of the event occuring at all and its usually measured between 0 and 1. if it moves closer to zero, that means the chances are very low and as it moves closer to one, the chances are very high (or quite high).
The probability basically can be calculated as
P (E) = Number of required outcomes / Number of possible outcomes
The number of required outcomes is the expected results from the experiment, in this case the required outcome is the probability or chances of picking a purple marble and a white marble. The number of possible outcomes is the total of all possibilties regardless of whether its part of your expected results or not.
Bowl 1 contains a total of 20 marbles, that means all possible outcomes are 20. There are however 4 purple marbles and that means the required outcomes are 4. Therefore the probabilty of picking a purple marble is calculated as follows;
P(Purple) = No of required Outcomes / No of possible Outcomes
P (Purple) = 4/20
P (Purple) = 1/5
P (Purple) = 0.2
Similarly, the probability or chance of picking a white marble from bowl 2 is calculated as follows;
P(White) = No of required outcomes / No of possible outcomes
P(White) = 6/20
P(White) = 3/10
P(White) = 0.3
At this point we need to know the probability of picking a purple AND a white marble, and this is done each time with replacement. That means the result of one event does not affect the result of the next, they are independent events.
To calculate the probability of independent events, you use the formula
P (Ind Events) = P(A) * P(B)
You multiply both results together, that is the result of the probabilty of event A times that of event B. Our A and B in this case are Purple and White. Therefore,
The probability of picking a purple and a white marble is derived as follows;
P [(W) * (P)] = 0.3 * 0.2
P [(W) * (P)] = 0.06
{Note that you have two decimals, hence your answer will have to be two decimal places}
If the probability of both events is derived as 0.06, then she has a 6% chance of drawing a purple marble from bowl 1 and a white marble from bowl 2. This can be used as a predictor, that is if she now draws both marbles from both bowls 200 times, the result predictably would be;
Prediction = Probability * Number of experiments
Prediction = 0.06 * 200
Prediction = 12
Does the set of numbers represent a Pythagorean Triple. 4,5,6YesNo
representNo
Explanation
to find if the numbers represent a Pythagorean triple, we need check if it is possible to make a rigth triangle with those side lengths
the bigger number will be the hypotenuse, then
Let
[tex]\begin{gathered} 6\rightarrow hypotenuse \\ 4\rightarrow side1 \\ 5\text{ }\rightarrow side2 \end{gathered}[/tex]now, the Pythagoras theorem is
[tex]\text{side}1^2+side2^2=hypotenuse^2[/tex]then , replace
[tex]\begin{gathered} 4^2+5^2=6^2 \\ 24+25=36 \\ 49=36,\text{ false, then 4.5,6 NOT represent a Pythagorean triple} \end{gathered}[/tex]I hope this helps you.
[tex]undefined[/tex]Monday - 8:00 to 12:15 and then 12:45 to 5:00Tuesday - 7:45 to 11:30 and then 12:15 to 6:00Wednesday - 8:15 to 12:00 and then 12:30 to 5:30Thursday - 8:00 to 12:00 and then 1:00 to 5:00Friday - 7:45 to 12:30 and then 1:00 to 7:15Total Hours for the week in Minutes-Total Hours for the week in DECIMAL -
we can start counting hour per day
Monday:4.25+4.25
Tuesday:3.75+5.75
wednesday:3.75+5
Thursdat:4+4
Friday:4.75+6.25
[tex]\begin{gathered} 8.5+9.25+8.75+8+11 \\ =45.5 \end{gathered}[/tex]so, 45.5 hours per week
and late multiply by 60 to find the minutes
[tex]\begin{gathered} 45.5\times60 \\ =2730 \end{gathered}[/tex]so, the total hours for the week in Minutes is 2730
In a certain county in New York state, the mean monthly utility bill per household is $295 with a standard deviation of $30. The monthly bill per household is normally distributed. If a random sample of 25 households is selected from this county, what is the probability that the sample mean monthly utility bill will be more than $290? Give your answer to four decimal places. [a]
Using
Given[tex]\begin{gathered} x=290 \\ \mu=295 \\ \sigma=30 \end{gathered}[/tex]Solution[tex]\begin{gathered} Z=\frac{290-295}{30} \\ \\ Probabilityofx>290:0.56618 \end{gathered}[/tex]The final answerCaroline has some dimes and some quaeters. she has a maximum of 15 coins worth at least $2.85 combined. if Caroline has 3 dimes determine all the possible values for the number of quarters she could have.
Answer:
The possible values for the number of quarters she could have is;
[tex]11\text{ and 12}[/tex]Explanation:
Given that Caroline has some dimes and some quarters.
she has a maximum of 15 coins worth at least $2.85 combined.
Let d and q represent the number of dimes and quarters she has.
1 dime = $0.10
1 quarter = $0.25
So, we have;
[tex]\begin{gathered} d+q\leq15\text{ ----------1} \\ 0.10d+0.25q\ge2.85\text{ ------2} \end{gathered}[/tex]if Caroline has 3 dimes;
[tex]d=3[/tex]substituting into equation 1 and 2;
[tex]\begin{gathered} d+q\leq15 \\ 3+q\leq15 \\ q\leq15-3 \\ q\leq12 \end{gathered}[/tex][tex]\begin{gathered} 0.10d+0.25q\ge2.85 \\ 0.10(3)+0.25q\ge2.85 \\ 0.30+0.25q\ge2.85 \\ 0.25q\ge2.85-0.30 \\ 0.25q\ge2.55 \\ q\ge\frac{2.55}{0.25} \\ q\ge10.2 \end{gathered}[/tex]Therefore;
[tex]10.2\leq q\leq12[/tex]So the possible values for the number of quarters she could have is;
[tex]11\text{ and 12}[/tex]A service station attendant is paid time-and-a-half for working over 40 hours per week. Last week the attendant worked 47 h and earned $580.75. Find the attendant's regular hourly wage.
the attendant's regular hourly wage is $11.50
Explanation:let the regular pay = p
time and the half is the amount paid for overtime:
time and the half = p + 1/2p = p + 0.5p
time and the half = 1.5p
40 hours is the normal hours. Hence, the cost per hour is P
7 hours is the over time. The cost per hour 1.5p
Total earned = $580.75
p(40) + 1.5p(7) = 580.75
40p + 10.5p = 580.75
50.5p = 580.75
divide both sides by 50.5:
50.5p/50.5 = 580.75/50.5
p = 11.5
Hence, the attendant's regular hourly wage is $11.50