Total owed to the business = $100,000
amount that could not be collected = $5000
Fraction of total not collected
[tex]\text{fraction not collected=}\frac{5000}{100000}=\frac{5}{100}=\frac{1}{20}[/tex]I really need help with this can somebody help me ?
Answer
a. Vertical shrink by a factor of 1/3
Step-by-step explanation
Function transformation
• a,f(x) vertically compresses f(x) when 0 < a < 1
Given the function:
[tex]f(x)=x^2[/tex]Multiplying f(x) by a = 1/3, we get:
[tex]\frac{1}{3}f(x)=\frac{1}{3}x^2=h(x)[/tex]Then, f(x) is vertically shrunk by a factor of 1/3
Find the perimeter of each polygon. Assumethat lines which appear to be tangent aretangent.13)7.81118.4
Answer: We have to find the perimeter of the provided triangle, the perimeter would be the sum of sides, which would be as follows:
[tex]\begin{gathered} P=S_1+S_2+S_3 \\ P=7.8+18.4+11 \\ P=37.2 \end{gathered}[/tex]the client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml. How many teaspoons should the nurse instruct the client to take?
Step 1
Given; The client is to receive cimetidine 300mg by mouth every 6 hours. The medication is available as cimetidine 300mg/5ml.
Required; How many teaspoons should the nurse instruct the client to take?
Step 2
[tex]\begin{gathered} 1\text{ teaspoon =5ml } \\ Patient\text{ takes 300mg/5ml or 300mg/teaspoon} \\ \frac{Required\text{ dosage in mg}}{Dosage\text{ in 1 teaspoon}}\times5ml \\ Required\text{ dosage in mg=300mg} \\ Dosage\text{ in 1 teaspoon=300mg} \\ \frac{300mg}{300mg}\times5ml=5ml \\ From\text{ the table 5ml is the equivalent of 1 teaspoon .} \end{gathered}[/tex]Thus, the client takes 300mg every six hours. This means that the nurse will instruct the client to take 1 teaspoon every 6 hours.
Answer;
[tex]1\text{ teaspoon every 6 hours}[/tex]102,410,000,000,000,000,000,000,000 in scientific notation round to two digits after the decimal
We have a big integer and want to write in scientific notation.
To do this we need to count how many places we need to move the decimal point.
In this case we need to move the decimal point to left so the exponent of 10 will be positive.
So,
[tex]\begin{gathered} 102,410,000,000,000,000,000,000,000=1.0241\cdot10^{29} \\ \text{Round to two digits after the decimal:} \\ 1.02\cdot10^{29} \end{gathered}[/tex]We move the decimal point 29 places to left so the exponent of 10 is 29.
using the gcf and the distributive property find the sum of 34+51
it would be 75 ur welcome
what is the sum of 141.2-79.83
Given:
141.2 - 79.83
Here, we are to subtract 79.83 from 141.2
Let's evaluate the given expression.
We have:
[tex]\begin{gathered} 141.20 \\ -79.83 \\ _{\text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \\ \text{ 61.37} \end{gathered}[/tex]ANSWER:
61.37
El contratista encargado de construir el
cerco perimetral desea saber la expresión
algebraica correspondiente al perímetro de
todo el lote
Medidas:
25p-8
40p+2
El perímetro del lote tiene una medida de 130 · p - 12 unidades.
¿Cuál es la longitud del cerco perimetral para un lote?
El perímetro es la suma de las longitudes de los lados de una figura, un rectángulo tiene cuatro lados, dos pares de lados iguales. En consecuencia, el perímetro del lote es el siguiente:
s = 2 · w + 2 · l
Donde:
w - Ancho del lote.l - Largo del lote.s - Perímetro del lote.Si sabemos que w = 25 · p - 8 y l = 40 · p + 2, entonces el perímetro del lote es:
s = 2 · (25 · p - 8) + 2 · (40 · p + 2)
s = 50 · p - 16 + 80 · p + 4
s = 130 · p - 12
El perímetro tiene una medida de 130 · p - 12 unidades.
ObservaciónNo se ha podido encontrar una figura o imagen asociada al enunciado del problema. Sin embargo, se puede inferir que el lote tiene una forma rectangular debido a las medidas utilizadas. En consecuencia, asumimos que la medida del ancho es igual a 25 · p - 8 unidades y del largo es igual a 40 · p + 2 unidades.
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Sample SpaceFind the number of outcomes in the following experiments. 1. Selecting a letter from the English alphabet
The English Alphabet consist of 26 letters. The number of outcome of the experiment therefore is 26 which consist of the sample space.
S = {A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}
Insert three arithmetic means between -16 and 4
To answer this question we will use the following formulas to compute n arithmetic means between 'a' and 'b':
[tex]\begin{gathered} A_1=a+\frac{b-a}{n+1}, \\ A_2=a+2\cdot\frac{b-a}{n+1}, \\ \ldots \\ A_n=a+n\cdot\frac{b-a}{n+1}\text{.} \end{gathered}[/tex]Substituting n=3, a=-16, and b=4 we get:
[tex]\begin{gathered} A_1=-16+\frac{4-(-16)}{3+1}, \\ A_2=-16+2\cdot\frac{4-(-16)}{3+1}, \\ A_3=-16+3\cdot\frac{4-(-16)}{3+1}\text{.} \end{gathered}[/tex]Simplifying the above results we get:
[tex]\begin{gathered} A_1=-16+\frac{4+16}{4}=-16+\frac{20}{4}=-11, \\ A_2=-16+2\cdot\frac{4+16}{4}=-16+\frac{40}{4}=-6, \\ A_3=-16+3\cdot\frac{4+16}{4}=-16+\frac{60}{4}=-1. \end{gathered}[/tex]Answer: -11, -6, and -1.
State if the given binomial is a factor of the given polynomial.Question #9
We can use the Factor Theorem to state if the given binomial is a factor of the given polynomial.
The factor theorem states that when f(c)=0 that means the remainder is zero and (x-c) must be a factor of the polynomial.
The given polynomial is:
[tex]k^3+8k^2+6k-12[/tex]Then if (k+2) is a factor of the polynomial, k+2=0, k=-2, f(-2) must be equal to 0.
Let's check:
[tex]\begin{gathered} f(k)=k^3+8k^2+6k-12 \\ f(-2)=(-2)^3+8(-2)^2+6(-2)-12 \\ f(-2)=-8+8\cdot4-12-12 \\ f(-2)=-8+32-24 \\ f(-2)=32-32 \\ f(-2)=0 \end{gathered}[/tex]Thus, (k+2) is a factor of the given polynomial.
Jason enjoys watching the squirrels in his neighborhood park. They eat the red oak acorns. After the city removed 4 diseased red oak trees, the population of squirrels decreased from 105 to 98 in one year. If the population continues to decline at the same rate, how many squirrels will live in the park in 15 years? First, calculate the rate of decay by subtracting the two populations and dividing the difference by the initial population. Then, use the formula A=a0e^kt
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given parameters
[tex]\begin{gathered} Initial\text{ squirrels}=105 \\ Num\text{ber of squirrels after one year}=98 \\ change\text{ in number of squirrels in a year}=105-98=7 \\ chan\text{ge in diseased oak trees}=y-4 \end{gathered}[/tex]STEP 2: Calculate the rate of decay (k)
[tex]\begin{gathered} rate\text{ of decay\lparen k\rparen}=\frac{Final\text{ population-Initial population}}{initial\text{ population}} \\ \text{By substitution,} \\ k=\frac{98-105}{105}=\frac{-7}{105}=-0.06666666\approx-0.0667 \end{gathered}[/tex]STEP 3: Calculate the number of squirrels after 15 years
[tex]\begin{gathered} A=a_0e^{kt} \\ a_0=105 \\ k=-0.0667 \\ t=15 \end{gathered}[/tex]By substitution,
[tex]A=105\cdot e^{-0.0667\times15}[/tex]By simplification,
[tex]\begin{gathered} \mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b} \\ =105\times \frac{1}{e^{15\times \:0.0667}} \\ \mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c} \\ =\frac{1\times \:105}{e^{1.0005}} \\ \mathrm{Multiply\:the\:numbers:}\:1\times \:105=105 \\ =\frac{105}{e^{1.0005}} \\ e^{1.0005}=2.71964 \\ =\frac{105}{2.71964} \\ \mathrm{Divide\:the\:numbers:}\:\frac{105}{2.71964}=38.60803 \\ =38.60803 \end{gathered}[/tex]By approximation, this leaves us with 34 squirrels
Completely factor the expression by grouping if possible 2xy+3x+10y+15
The required factor of the given expression is given as (2y + 3)(x + 3).
Given that,
The factor of the given expression 2xy+3x+10y+15 is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here
= 2xy+3x+10y+15
Simplifying through factorization,
= x(2y + 3) + 5(2y + 3)
= (2y + 3)(x + 3)
Thus, the required factor of the given expression is given as (2y + 3)(x + 3).
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Help me answer these thank u :)
6. -2
7.-38
8.-15
9.0
10.-13
11.-30
12.38
13.33
14.-23
The first 19 terms of the sequence 9, 2, -5, -12,... find the sum of the arithmetic sequence
To find the sum of the ari
A house has increased in value by 35% since it was purchased. If the current value is S432,000, what was the value when it was purchased?
The value of the house when it was purchased = $32000
Explanation:The original percentage value = 100%
The current percentage value = 100% + 35% = 135%
Current value = $432000
Original value = x
[tex]\begin{gathered} The\text{ current value =}\frac{135}{100}\times The\text{ original value} \\ \\ 432000=1.35\times x \\ \\ x=\frac{432000}{1.35} \\ \\ x=$ 320000 $ \end{gathered}[/tex]The value of the house when it was purchased = $32000
The cost of 15 toys is $225. Identify the equation that represents this situation.
Question:
Solution:
Let us denote by c the cost of each toy. Then, according to the problem, the cost of 15 toys would be:
[tex]15c\text{ = 225}[/tex]So, we can conclude that the correct answer is:
[tex]15c\text{ = 225}[/tex]In the equation Q = 45e1.031a quantity Q is changing over time t.(a) What is the quantity at timet = 0?(b) Is the quantity increasing or decreasing over time?(c) What is the percent per unit time continuous growth or decay rate?
(a) The equation is given as Q=45e^1.03t
where e=2.718
Taking t=0 the equation will be :
[tex]Q=45e^{1.03\ast0}[/tex]This will give;
[tex]Q=45\ast2.718^0[/tex]Q=45
In the scoring for a game, points can be negative and positive. There were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times. How many more times would 5.5 points need to be scored to have a total gain greater than 15 points?
A. 1
C. 3
B. 2
D. 4
The number of times that 5.5 points is need to be scored to have a total gain greater than 15 points is A. 1
How to calculate the value?From the information, it was stated that there were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times.
In this case, the entire score will be:
= (-3.25 × 4) + (-2.75 × 5) + (3 × 2) + (5.5 ×4)
= -13 - 13.75 + 6 + 22
= 11.25
Therefore, the times that 5.5 points is needed to be scored to have a total gain greater than 15 will be 1 time since 11.25 + 5.5 = 16.75. This is more than 15.
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1.In hockey, a player gets credited with a "point" in their statistics when they get an assist or goal.The table shows the number of assists and number of points for 15 hockey players after a season.assistspoints222816184672292691322allo San818131750712173427581834Make a scatter plot of this data. Make sure to scale and label the axes
From the information given, the number of points gotten depends on the number of assists. this means that the independent variable, x which would be on the horizontal axis is the number of assists and the dependent variable, y which would be on the vertical axis is the number of points. We would plot these values on the scatter plot. the plot is shown below
The number of points is on the vertical axis.
The number of assists is on the horizontal axis
How do you find the square root of -6 by imaginary numbers
To find the square root of a negative number use the next:
[tex]\sqrt{-1}=i[/tex]For -6:
You can write -6 as the product of 6 and -1:
[tex]\sqrt{\left(6\right)*\left(-1\right)}[/tex]The square root of a product is the same as the product of the square root if each of the factors:
[tex]=\sqrt{6}*\sqrt{-1}[/tex]As the square root of 6 is not a exact number (it has many decimals) you leave the square root of 6 as it is. The square root of -1 is i; then, the square root of -6 is:
[tex]\begin{gathered} =\sqrt{6}*i \\ =\sqrt{6}i \end{gathered}[/tex]Then, the square root of -6 is: (√6)iI'm not sure what to do for this question I have already tried could you help me with this?
1) Take into account that a linear relation can be written as follow:
y = mx + b
where m is the slope of the line and the constant b the y-coordinate of the y-intercept.
Due to Rocco started to count from a distance of 4 miles, this is a constant number, which is equivalent to b, that is, b = 4.
If the constant rate of the walk is 3 miles per 2 hours, then, m = 3/2 (because the slope is also a constant rate of change).
Then, you have the following linear equation for the relation between the distance traveled by Rocco and the time.
y = 3/2*x + 4
y is the number of miles of the Rocco walking
x is the time (in hours) he takes for the walking
2) Now, based on the previous equation, you have for the table:
3) The relation between the given variables is proportional because a change in x makes that y changes too.
The distance traveled by Rocco is given by the value of y when x = 4. As you can notice on the table, such a distance is 10 miles.
A randomly generated list of integers from 0 to 7 is being used to simulate an event, with the numbers 0, 1, 2, and 3 representing a success. What is the estimated probability of a success? O A. 25% OB. 50% O C. 80% O D. 43%
The total numbers of integers used is 7 + 1 = 8 (since we are using ubtewgers from 0 to 7).
If 0, 1, 2 and 3 represents succes, we have 4 integers of the 8 total that are success, thus, the theoretical probability is:
[tex]P=\frac{4}{8}=0.5[/tex]So the probability os success is 0.50 = 50%.
Calculate the five-number summary and the IQR from the following values given: {17, 20, 21, 25, 25, 29, 40}
Answer:
• 17, 20, 25, 29 and 40
,• IQR=9
Explanation:
(a)Given the set of values:
{17, 20, 21, 25, 25, 29, 40}
• The minimum value = 17
The first quartile
The first quartile is the median of the lower half of the data set.
The lower half of the data set = 17, 20, 21
• Therefore, the first quartile =20
The Median
The median is the number in the middle of the set of values.
The number in the middle is 25, therefore:
• Median = 25
The third quartile
The third quartile is the median of the upper half of the data set.
The upper half of the data set = 25, 29, 40
• Therefore, the third quartile =29
Finally, Maximum Value = 40.
The five-number summary of the set of values is: 17, 20, 25, 29 and 40
(b)Interquartile Range
Interquartile Range = Third Quartile - First Quartile
=29 - 20
IQR=9
Are there no more tutors for mathematics, I can’t seem to find the option anymore for a tutor.
A quadratic equation is represented graphically as:
[tex]y=a(x-h)^2+k[/tex]Here the graph represents the parabola where (h,k) is the vertex of the parabola.
Put any value of h, k and a to get the graph as follows:
The graph of a quadratic equation is parabolic in nature.
Suppose that you have a quadratic equation given by:
[tex]y=x^2-5x+6[/tex]Convert the equation into perfect square by completing the square method
[tex]\begin{gathered} y=(x^2-5x+\frac{25}{4})+6-\frac{25}{4} \\ y=(x-\frac{5}{2})^2-\frac{1}{4} \end{gathered}[/tex]This is the method of conversion of quadratic to plot the graph.
Two companies provide service in a community.• The total cost of a service call for x hours of labor at company A is modeled byy = 28x+ 32.5.• The initial charge for a service call at company B is $3 less than at company A, but their hourly rate is 25% greater.What is the expected total cost of a service call for 6 hours of labor at company B?
Answer:
The expected total cost of a service call for 6 hours of labor at company B is $239.5
Step-by-step explanation:
To solve this, we'll find the expression that models the cost at company B.
First, we'll calculate the hourly rate. We know that is 25% greater than the $28 rate from company A, so we can use a rule of three as following:
This way,
[tex]\begin{gathered} x=28\times\frac{125}{100} \\ \\ \Rightarrow x=35 \end{gathered}[/tex]Therefore, we'll have that the hourly rate for company B is $35.
Now, we know that the charge for service is $3 less than at company A. This way,
[tex]32.5-3=29.5[/tex]We can conclude that the charge for service at company B is $29.5
Using this data, we'll have that the expression that models the cost for company B is:
[tex]y=35x+29.5[/tex]Using x = 6 (six hours of labor),
[tex]\begin{gathered} y=35(6)+29.5 \\ \\ \Rightarrow y=239.5 \end{gathered}[/tex]Therefore, we can conclude that the expected total cost of a service call for 6 hours of labor at company B is $239.5
Use the commutative property of multiplication to write an equivalent expression to 69xuse the distributive property to write an equivalent expression to 8(c+5) that has no grouping symbols.
Answer
69x = 69 × x = x × 69
8 (c + 5)
= 8c + 40
Explanation
The commutative property of multiplication for two numbers a and b, is given as
a × b = b × a = ab
69x = 69 × x = x × 69 = 69x
Question 2
The distributive property for openingh brackets involving three numbers a, b and c is given as
a (b + c)
= ab + ac
So, for this question
8 (c + 5)
= 8c + 40
Hope this Helps!!!
Calculate each percent increase or percent decreases Round to the nearest whole percent if necessary 1. original amount: 30, new amount: 45 2. original amount: 12, new amount: 16 3. original amount: 17 new amount: 21 4. original amount: 85, new amount: 56 5. original amount: 48, new amount: 37 6. original amount: 124, new amount: PLS HELP ME!!!
The percentage increase is 50%
Here, we want to calculate the percentage increase or decrease
To know if it is a decrease or an increase, we use the following simple logic.
If new amount is greater than original amount, then it is an increase.
If new amout is less than original amount, then it is a decrease
For the first question, we can see that the new amount is greater than the old amount
This indicates an increase
Mathematically;
[tex]\text{percentage increase = }\frac{(new\text{ amount - original amount)}}{\text{old amount}}\text{ }\times\text{ 100 percent}[/tex]According to the first question, new amount = 45 while old amount = 30
so;
percentage increase = (45-30)/30 * 100%
= 15/30 * 100% = 100%/2 = 50%
Which of the following point-slope form equations could be produced with the points (3, 4) and (1, -7)?
Answer:
y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~
( 3 , 4 )
( 1 , - 7 )
m = [tex]\frac{-7-4}{1-3}[/tex] = [tex]\frac{-11}{-2}[/tex] = [tex]\frac{11}{2}[/tex]
y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )
A certain drug dosage calls for 330 mg per kg per day and is divided into four doses (1 every 6 hours). If a person weighs 210 pounds, how many milligrams of the drug should he receive every 6 hours?Round your answer to the nearest milligram. Do not include units with your answer.
First, we convert the 210 pounds to kilograms as the dose is given in mg per kg.
Recall that:
[tex]1pound=0.453592\text{ kilograms.}[/tex]Therefore:
[tex]210\text{ pounds=95.2544 kilograms.}[/tex]The dose call for 330 mg per kg, therefore, to get the dose for 95.2544 kg, we multiply by 95.2544:
[tex]330*95.2544\text{ mg=31433.952mg.}[/tex]Finally, dividing by 4 we get the dose the person should receive every 6 hours:
[tex]7858.488mg\approx7858mg.[/tex]Answer: [tex]7858.[/tex]A cylinder sits on top of the rectangular prism. What is the combined volume? (use the Pi, round to the nearest tenth of an inch) ______ in3
The combined volume is:
[tex]V=V_{rp}+V_c[/tex]The volume of the rectangular prism is:
[tex]V_{rp}=l\cdot w\cdot h[/tex]The volume of a cylinder is:
[tex]V_c=\pi\cdot r^2\cdot h[/tex]Then, the combined volume is:
[tex]\begin{gathered} V=l_{rp}\cdot w_{rp}\cdot h_{rp}+\pi\cdot r^2\cdot h_c \\ \\ V=10m\cdot5m\cdot3m+\pi\cdot(2m)^2\cdot4m \\ V=150m^3+16\pi m^3 \\ V=(150+16\pi)m^3 \\ \\ V\approx200.3\text{ }m^3 \end{gathered}[/tex]Turn into inches:
[tex]200.3m^3\cdot\frac{61023.7in^3}{1m^3}=12223047in^3[/tex]Then, the volume in inches is 12,223,047 cubic inches (200.3 cubic meters)
