The venue measures 40 ft by 75 ft . This means the venue has the shape of a rectangle. A rectangle
Jan plans to tell two people each day and will ask that person to tell two other people each day through the day of the opening, and so on. Assume that each new person who hears about the soft opening is also asked to tell two other people each day through the day of the opening and that each one starts the process of telling their friends on the day after he or she first hears. When should Jan begin telling others about the soft opening in order to have at least 700 people know about it by the day it occurs?
Explanation:
From the given question, we can sketch the pattern observed
The figure above helps show how the number of people increases
Initially, Jan tells 2 more people, then the two people tell two more people, then they also tell two more people
Thus
we can see that the model is given by
[tex]\begin{gathered} (2)^n \\ where\text{ n is the number of days} \end{gathered}[/tex]In order to have at least 700 (it also means a minimum of 700), we will have the equation
[tex]2^n\ge700[/tex]We then solve for n
Taking the log of both sides
[tex]n\text{ }log2\ge log700[/tex][tex]n\ge\frac{log700}{log2}[/tex]So that
[tex]\begin{gathered} n\ge\frac{2.845}{0.301} \\ \\ n\ge9.451 \end{gathered}[/tex]So, the number of days will be at least 10 days (Rounded to the nearest whole day )
3 1/2 ÷ 47/815/88/73/4
the given expression is,
[tex]\begin{gathered} 3\frac{1}{2}\div4=\frac{7}{2}\div4 \\ =\frac{\frac{7}{2}}{4}=\frac{7}{8} \end{gathered}[/tex]so the answer is option A
Solve x4 + 8x2 + 15 = 0.X = +15 and x = 113x = 5 and x = 13x = 113 and x = 15X = 3/1/3 and x = 1115
Answer
Option D is correct.
x = ±i√(5) OR ±i√(3)
Explanation
The question wants us to solve
x⁴ + 8x² + 15 = 0
To solve this, we first say that
Let x² = y
So that,
x⁴ = (x²)² = y²
So, the equation becomes
y² + 8y + 15 = 0
This is a simple quadratic equation, we then solve this
y² + 8y + 15 = 0
y² + 3y + 5y + 15 = 0
y (y + 3) + 5 (y + 3) = 0
(y + 5) (y + 3) = 0
y + 5 = 0 OR y + 3 = 0
y = -5 OR y = -3
But, Recall that x² = y
If y = -5
x² = y = -5
x² = -5
x = √(-5)
If y = -3
x² = y = -3
x² = -3
x = √(-3)
So,
x = √(-5) OR x = √(-3)
Note that
√(-1) = i
√(-5) = √(-1) × √(5)
= i√5
And
√(-3) = √(-1) × √(3)
= i√3
Hence
x = ±i√(5) OR ±i√(3)
Hope this Helps!!!
An advertising company plans to market a product to low-income families. A study states that for a particular area the mean income per family is $25,174 and the standard deviation is $8,700. If the company plans to target the bottom 18% of the families based on income, find the cutoff income. Assume the variable is normally distributed.
log (2x+ 9) = 1+ log(x- 8)
x = 11.125
STEP - BY - STEP EXPLANATION
What to do?
Solve the given equation.
Given:
log (2x+ 9) = 1+ log(x- 8)
To solve, we will follow the steps below:
Step 1
Re-arrange by subtracting log(x-8) from both-side of the equation.
[tex]log(2x+9)-log(x-8)=1[/tex]Step 2
Apply the law of logarithm that is applicable to the given problem.
[tex]log\frac{(2x+9)}{(x-8)}=1[/tex]Step 3
Replace 1 by log10
Step 4
[tex]log\frac{(2x+9)}{(x-8)}=log10[/tex]Step 5
Cancel-out the log from both-side of the equation.
[tex]\frac{2x+9}{x-8}=10[/tex]Step 6
Cross - multiply
[tex]2x+9=10(x-8)[/tex]Step 7
Open the parenthesis.
[tex]2x+9=10x-80[/tex]Step 8
Collect like term.
[tex]10x-2x=80+9[/tex][tex]8x=89[/tex]Step 9
Divide both-side of the equation by 8
[tex]\frac{8x}{8}=\frac{89}{8}[/tex][tex]x=11.125[/tex]Therefore, the value of x is 11.125
As cashier, you need to record all over times you worked in hours. If you worked 330 mnts of over time how many hours will you record ?
First, we need the next equivalence
1 hour = 60 min
we have 330 min in order to know the number of hours we need to divide the 330 min between 60
[tex]\frac{330}{60}=5.5[/tex]He will record 5.5 hours
34 Sat purchased some art supplies and cord stock in order to make greeting cards. The graphbelow shows the relationship between the number of cards Sat makes and the total cost etthe materials used te make the cardsCost of Noking Greeting CardsTotal Cost(dollars)2 4 6 8 10Number of Cards MadeBased on the graph what will be the total cost of making 25 greeting cards?*2.50G$50.00N $52.50$15.00
step 1
Find the slope
we have the points
(3,4) and (7,6)
m=(6-4)/(7-3)
m=2/4
m=$0.5 per card
the equation of the line in slope intercept form is equal to
y=mx+b
we have
m=0.50
b=?
point (3,4)
substitute
4=0.5(3)+b
b=4-1.50
b=2.50
y=0.50x+2.5
so
For x=25 cards
substitute
y=0.50(25)+2.50
y=15.00
answer is the option JFind the volume of a cube with a side length of 2.8 in, to the nearest tenth of a cubic inch (if necessary).
Given:
Length of side = 2.8 in
Let's find the volume of the cube.
To find the volume of a cube, apply the formula:
[tex]V=a^3[/tex]Where:
a is the side length = 2.8 in
Hence, to find the volume, we have:
[tex]\begin{gathered} V=2.8^3 \\ \\ V=2.8*2.8*2.8 \\ \\ V=21.952\approx22.0\text{ in}^3 \end{gathered}[/tex]Therefore, the volume of the cube is 22.0 cubic inch.
ANSWER:
22.0 in³
Which value of w makes 6W + 7 = 12 true
6W + 7 = 12
to solve this, just isolate W
[tex]\begin{gathered} 6W+7=12 \\ \text{substract 7 in both sides} \\ 6W+7-7=12-7 \\ 6W=5 \\ divide\text{ each side by 6} \\ \frac{6W}{6}=\frac{5}{6} \\ W=\frac{5}{6} \end{gathered}[/tex]so, the answer is w=5/6
For the function f(x) = 6e^x, calculate the following function values:f(-3) = f(-1)=f(0)= f(1)= f(3)=
Consider the given function,
[tex]f(x)=6e^x[/tex]Solve for x=-3 as,
[tex]\begin{gathered} f(-3)=6e^{-3} \\ f(-3)=6(0.049787) \\ f(-3)=0.2987 \end{gathered}[/tex]Thus, the value of f(-3) is 0.2987 approximately.
Solve for x=-1 as,
[tex]\begin{gathered} f(-1)=6e^{-1} \\ f(-1)=6(0.367879) \\ f(-1)=2.2073 \end{gathered}[/tex]Thus, the value of f(-1) is 2.2073 approximately.
Solve for x=0 as,
[tex]\begin{gathered} f(0)=6e^0 \\ f(0)=6(1) \\ f(0)=6 \end{gathered}[/tex]Thus, the value of f(0) is 6 .
Solve for x=1 as,
[tex]\begin{gathered} f(1)=6e^1 \\ f(1)=6(2.71828) \\ f(1)=16.3097 \end{gathered}[/tex]Thus, the value of f(1) is 16.3097 approximately.
Solve for x=3 as,
[tex]\begin{gathered} f(3)=6e^3 \\ f(3)=6(20.0855) \\ f(3)=120.5132 \end{gathered}[/tex]Thus, the value of f(3) is 120.5132 approximately.
A student takes out 2 loans to pay for college. One loan at 8% interest and the other at 9% interest. The total amount borrowed is $3,500, and the interest after 1 year for both loans is $294. Find the amount of each loan.
The amount of each loan are $2,100 and $1,400.
What is mean by Simple interest?
The simple interest is defined as;
Simple interest = P r t
Where, P is principal amount.
r is rate and t is time period.
Given that;
Student take 2 loans for pay the college.
One loan at 8% interest and the other at 9% interest.
And, The total borrowed amount = $3,500
and, The interest loan = $294
Let The first amount of loan = x
And, The other amount of loan = y
So, We can formulate;
x + y = $3,500 ..... (i)
And, The interest loan = $294
So, We can formulate;
8x/100 + 9y/100 = $294
8x + 9y = 29400 ... (ii)
Solve equation (i) and (ii) , we get;
Multiply by 8 in equation (i) and subtract from (ii), we get;
y = $1400
Hence,
x + y = $3,500
x + 1400 = 3500
x = 3500 - 1400
x = $2,100
Therefore, The amount of each loan are $2,100 and $1,400.
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I will show you a pic
GIven the table above :
We have that
x y
2 8
4 4
6 0
8 4
The table represents a Non - Linear Function
Reason: It is because there is no constant ratio or proportion between x and y.
I need help with the entire problem. The question is about a sketchy hotel.
Let d and s be the cost of a double and single- occupancy room, respectively. Since a double-occupancy room cost $20 more than a single room, we can write
[tex]d=s+20\ldots(A)[/tex]On the other hand, we know that 15 double-rooms and 26 single-rooms give $3088, then, we can write
[tex]15d+26s=3088\ldots(B)[/tex]Solving by substitution method.
In order to solve the above system, we can substitute equation (A) into equation (B) and get
[tex]15(s+20)+26s=3088[/tex]By distributing the number 15 into the parentheses, we have
[tex]15s+300+26s=3088[/tex]By collecting similar terms, it yields,
[tex]41s+300=3088[/tex]Now, by substracting 300 to both sides, we obtain
[tex]41s=2788[/tex]then, s is given by
[tex]s=\frac{2788}{41}=68[/tex]In order to find d, we can substitute the above result into equation (A) and get
[tex]\begin{gathered} d=68+20 \\ d=88 \end{gathered}[/tex]Therefore, the answer is:
[tex]\begin{gathered} \text{ double occupancy room costs: \$88} \\ \text{ single occupancy room costs: \$68} \end{gathered}[/tex]POSSIBLE POINTS: 1One-half of a number increased by 16 is 4 less than two-thirds of the number. What is the number?
Let the number be x.
[tex]\begin{gathered} \frac{1}{2}x+16=\frac{2}{3}x-4 \\ \\ \frac{2}{3}x-\frac{1}{2}x=20 \\ \frac{4-3}{6}x=20 \\ \frac{1}{6}x=20 \\ x=120 \end{gathered}[/tex]The number is 120
write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the equation(-3, -5); y = -5x+2
The equation is y = -5x-20.
GIven:
The equation is, y = -5x + 2.
A point on the line is (-3, 5).
The objective is to write an equation that passes throught the point and parallel to the given equation.
For parallel lines the product of slope values will be equal.
From the given equation, consider the slope of the equation as, m1 = -5.
Then, the slope of the parallel line will also be, m2 = -5.
Then, the equation of parallel line can be written as,
[tex]\begin{gathered} y=m_2x+b \\ y=-5x+b \end{gathered}[/tex]Here b represents the y intercept of the parellel line.
To find the value of b, substitute the given points in the above equation.
[tex]\begin{gathered} -5=-5(-3)+b \\ -5=15+b \\ b=-5-15 \\ b=-20 \end{gathered}[/tex]Now, substitute the value of b in the equation of parellel line.
[tex]y=-5x-20[/tex]Hence, the equation of parellel line is y = -5x-20.
Find the length of the arc. Use 3.14 for it.270°8 cm
The radius of circle is r = 8 cm.
The arc is of angle 270 degree.
The formula for the arc length is,
[tex]l=2\pi r\cdot\frac{\theta}{360}[/tex]Determine the length of the arc.
[tex]\begin{gathered} l=2\cdot3.14\cdot8\cdot\frac{270}{360} \\ =37.68 \end{gathered}[/tex]So lenth of the arc is 37.68.
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 4 liters of synthetic oil. In order to make 531 litersof Petrolyn oll, how many liters of synthetic oil are needed?
The ratio 4 : 5 means that in every 9 liters of oil, we will have 4L of synthetic oil and 5L of natural oil.
Divide the 531 by 9 to get how many times we have to amplify the ratio:
[tex]\frac{531}{9}=59[/tex]Multiply the ratio by 59:
[tex]4\colon5\rightarrow(4)(59)\colon(5)(59)\rightarrow236\colon295[/tex]Meaning that for the 531L of oil, 236L would be synthetic and 295L natural.
Answer: 236 Liters.
What is the explicit rule for the nth term of the geometric sequence? Thanks
Solution.
Given the sequence
[tex]3,18,108,648,3888[/tex]Test which kind of sequence it is
[tex]\begin{gathered} \frac{18}{3}=6 \\ \frac{108}{18}=6 \\ The\text{ sequence has a common ratio which is 6. } \\ Thus,\text{ it is a geometric sequence} \\ \end{gathered}[/tex][tex]\begin{gathered} The\text{ nth term of a geometric sequence can be determined by the formula} \\ a_n=ar^{n-1} \\ where\text{ a = 1st term} \\ r=common\text{ ratio} \end{gathered}[/tex][tex]a_n=3(6^{n-1})[/tex][tex]The\text{ answer is a}_n=3(6^{n-1})[/tex]Mean player age Mean Absolute Team Three golf teams wanted to compare the ages of their players. Each team calculated their players' mean age in years and the mean absolute deviation of their ages. They displayed the results in this table. 9.5 45 Appleton Coalvale 31 15.9 Which statements are true? Summerton 43 16.1 Select each correct answer. Team Coalvale's players ages and Team Summerton's players ages vary about the same amount Team Summerton's players ages and Team Appleton's players ages vary about the same amount Team Appleton's players ages vary less than do Team Summerton's players ages. Team Appleton's players ages vary more than do Team Coalvale's players ages. a ? 7+ O i JOTE to search
Given:
• Appleton: Mean = 45; Mean Absolute deviation = 9.5
,• Coalvale: Mean = 31; Mean Absolute deviation = 15.9
,• Summerton: Mean = 43; Mean Absolute deviation = 16.1
Using the given data, let's select the correct statements.
From the data we can see the difference between the Mean Absolute Deviations of team Coalvale and Summerton is (16.1 - 15.9) = 0.2
This means the ages of team Coalvale and Summerton vary about the same about.
The Mean Absolute deviation of Appleton is far from other mean absolute deviation. This means the players ages for team Appleton vary less than others.
Therefore, the correct statements are:
• Team Coalvale's players ages and Team Summerton's players ages vary about the same amount.
• Team Appleton's players ages vary less than do Team Summerton's players ages.
ANSWER:
• Team Coalvale's players ages and Team Summerton's players ages vary about the same amount.
• Team Appleton's players ages vary less than do Team Summerton's players ages.
ok so the question is Write an expression to rubbers in the area of the figure the figure is a right triangle with 2X -2 and 4X plus 2 in the answer to that is 4X to the power of 2 - 2X -2 and that's part a and amp RP is what would the area be if X equals negative 2
ANSWERS
a) A = 4x² - 2x - 2
b) if x = -2, A = 18 units²
EXPLANATION
The area of a triangle is the length of the base, multiplied by its height and divided by 2:
[tex]A=\frac{b\cdot h}{2}[/tex]In this triangle, b = 4x + 2 and h = 2x - 2. The area is:
[tex]A=\frac{(4x+2)(2x-2)}{2}[/tex]We can simplify this expression. First we have to multiply the binomials in the numerator:
[tex]\begin{gathered} A=\frac{4x\cdot2x-4x\cdot2+2\cdot2x-2\cdot2}{2} \\ A=\frac{8x^2-8x+4x-4}{2} \\ A=\frac{8x^2-4x-4}{2} \end{gathered}[/tex]Now, using the distributive property for the division:
[tex]\begin{gathered} A=\frac{8x^2}{2}-\frac{4x}{2}-\frac{4}{2} \\ A=4x^2-2x-2 \end{gathered}[/tex]For part b, we just have to replace x with -2 in the expression above and solve:
[tex]\begin{gathered} A=4(-2)^2-2(-2)-2 \\ A=4\cdot4+4-2 \\ A=16+2 \\ A=18 \end{gathered}[/tex]zero and negative exponentswrite in simplest form without zero or negative exponents
We have the following rule for exponents:
[tex]a^0=1[/tex]then, in this case we have:
[tex](-17)^0=1[/tex]i need help please help
Answer:
I think d)
Step-by-step explanation:
if A (0, 2) and B (2, 0) dilation is a transformation, which is used to resize the object, so it can only mean that both are bigger and like the same number, hope that makes sense
A rectangle is placed around a semicircle as shown below. The width of the rectangle is . Find the area of the shaded region.Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Solution
Step 1
Write the given data:
Radius r of the semi-circle = 4 yd
Width of the rectanhle = 4 yd
Length of the rectangle = 2 x 4 = 8 yd
Step 2
Write the formula for the area of the shaded region:
[tex]\begin{gathered} Area\text{ of the shaded region} \\ =\text{ Area of a rectangle - Area of the semi-circl} \\ =\text{ W }\times\text{ L - }\frac{\pi r^2}{2} \\ =\text{ 4}\times\text{ 8 - }\frac{3.14\times4^2}{2} \\ =\text{ 32 - 25.12} \\ =\text{ 6.88 yd}^2 \end{gathered}[/tex]Final answer
6.88
What point in the feasible reign maximizes the objective function? constraints: x => 0 y => 0 y<= x - 4 x + y <= 6
Objective Function: C = 2x + y
The point in the feasible region maximizes the objective function is (5, 1)
How to determine the feasible region?The given parameters are
Objective function: C = 2x + y
Subject to (i.e. the constraints)
x >= 0, y >= 0
y <= x - 4, x + y <= 6
Represent y <= x - 4, x + y <= 6 as equations
y = x - 4 and x + y = 6
Substitute y = x - 4 in x + y = 6
So, we have
x + x - 4 = 6
Evaluate the like terms
2x = 10
This gives
x = 5
Substitute x = 5 in y = 6 - x
y = 6 - 5
Evaluate
y = 1
So, we have
(x, y)= (5, 1)
Hence, the coordinates is (5, 1)
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Consider the function f(x) = 6 - 7x ^ 2 on the interval [- 6, 7] Find the average or mean slope of the function on this interval , (7)-f(-6) 7-(-6) = boxed |
Answer:
• Mean Slope = -7
,• c=0.5
Explanation:
Given the function:
[tex]f\mleft(x\mright)=6-7x^2[/tex]Part A
We want to find the mean slope on the interval [-6, 7].
First, evaluate f(7) and f(-6):
[tex]\begin{gathered} f(7)=6-7(7^2)=6-7(49)=6-343=-337 \\ f(-6)=6-7(-6)^2=6-7(36)=6-252=-246 \end{gathered}[/tex]Next, substitute these values into the formula for the mean slope.
[tex]\begin{gathered} \text{ Mean Slope}=\frac{f(7)-f(-6)}{7-(-6)}=\frac{-337-(-246)}{7+6}=\frac{-337+246}{13} \\ =-\frac{91}{13} \\ =-7 \end{gathered}[/tex]The mean slope of the function over the interval [-6,7] is -7.
Part B
Given the function, f(x):
[tex]f\mleft(x\mright)=6-7x^2[/tex]Its derivative, f'(x) will be:
[tex]f^{\prime}(x)=-14x[/tex]Replace c for x:
[tex]f^{\prime}(c)=-14c[/tex]Equate f'(c) to the mean slope obtained in part a.
[tex]-14c=-7[/tex]Solve for c:
[tex]\begin{gathered} \frac{-14c}{-14}=\frac{-7}{-14} \\ c=0.5 \end{gathered}[/tex]The value of c that satisfies the mean value theorem is 0.5.
I already wrote the answer I just need you to work it out for me please and thank you
Answer:
[tex]A=470\frac{1}{4}ft^2[/tex]Detailed Explanation: The area of the figure provided is the sum of two areas, a rectangle, and a triangle:
The total area is calculated next, and the necessary steps are shown as follows
[tex]\begin{gathered} A=A_1+A_2 \\ A_1=\frac{1}{2}(b\cdot h)=\frac{1}{2}\cdot\lbrack(25ft-22.5ft)\times19.8ft\rbrack \\ A_1=\frac{1}{2}\cdot\lbrack2.5ft\times19.8ft\rbrack=\frac{49.5ft^2}{2}=24.75ft^2 \\ A_1=24.75ft^2 \\ A_2=w\cdot h=22.5ft\cdot19.8ft=445.5ft^2 \\ A_2=445.5ft^2 \\ \therefore\Rightarrow \\ A=A_1+A_2=24.75ft^2+445.5ft^2 \\ A=470.25ft^2 \\ A=470\frac{1}{4}ft^2 \end{gathered}[/tex]I need help with my math
Answer:
The fourth choice: y+3 = 1(x+2); y= x-1
Explanation:
The point slope form of a linear equation is
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point on the line and m is the slope.
Now we first calculate the slope.
[tex]m=\frac{3-(-3)}{4-(-2)}=\frac{6}{6}=1[/tex]therefore, we have
[tex]y-y_0=1(x-x_0)[/tex]Now we use (x0, y0) = (-2, -3) and get
[tex]y-(-3)_{}=1(x-(-2))[/tex][tex]\boxed{y+3=1\mleft(x+2\mright)}[/tex]which is our equation in point-slope form.
Now, we convert the equation above into the slope-intercept form.
Subtracting 3 from both sides gives
[tex]y+3-3=x+2-3[/tex][tex]\boxed{y=x-1}[/tex]which is the equation in slope-intercept form.
Hence, the answer to the question is
[tex]y+3=1(x+2);y=x-1[/tex]which is the fourth option.
You are clinic manager. You must schedule the equivalent of 1 1/2 nurses for each doctor on a shift, The friday day shift has 6 doctors scheduled How many nurses you will you need to schedule?
Data Given:
Nurses = 1 1/2 of each doctor
This can be interpreted as
[tex]\begin{gathered} 1\frac{1}{2}\text{ = }\frac{3}{2} \\ \\ 1\text{ Doctor requires }\frac{3}{2}\text{ times nurses} \end{gathered}[/tex]If there are 6 doctors in the day shift, then there will be
[tex]\frac{3}{2}\text{ x 6 nurs}es[/tex]=>
[tex]\begin{gathered} \frac{3\text{ x 6}}{2} \\ \\ =\text{ 3 x 3 } \\ \\ =\text{ 9 nurses} \end{gathered}[/tex]This means that I will have to schedule 9 nurses for the day shift on Friday
pls help i Dont get it
Answer:
what do you need
Step-by-step explanation:
according to recent study 7 out of every 500 Americans aged 13-17, years are vegetarian.in a group of 350 13 to 17- years old about how many would you expect to he vegetarian
7 out of every 500 Americans aged 13 -17 years are vegetarians
This implies that in a group of 500 Americans , 7 Americans that are within the age range of 13 - 17 years are vegetarians
7 ======== 500
x ======== 350
Introduce cross multiplication
7 x 350 = x * 500
2450 = 500x
Divide both sides by 500
2450/500 = 500x/ 500
x = 4.9
Approximately, 5
5 vegetarians aged 13 - 17 years will be present is in a group of 350 Americans
The answer is 5
