SOLUTION
Now, we don't know the scores for his first three tests. But we are told that the average score for the first three tests was 80.
So, let the scores of the first three tests be a, b, and c. That means
[tex]\frac{a+b+c}{3}=80[/tex]Also, let's assume the total score for his first three tests was x, This means that
[tex]\begin{gathered} a+b+c=x \\ or \\ x=a+b+c \end{gathered}[/tex]Comparing with the first equation it means that
[tex]\begin{gathered} \frac{a+b+c}{3}=80 \\ \frac{x}{3}=80 \\ x=3\times80 \\ x=240 \end{gathered}[/tex]Now we are asked "What must he score on his next test to raise his average to 84?"
So this means the total tests becomes 4. Hence
[tex]\begin{gathered} \frac{a+b+c+d}{4}=84 \\ \frac{x+d}{4}=84 \\ \frac{240+d}{4}=84 \\ 240+d=84\times4 \\ 240+d=336 \\ d=336-240 \\ d=96 \end{gathered}[/tex]So he must score 96 to raise his average score to 84.
Hence, the answer is 96
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]Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone. Any unused data will roll over to the next cycle. The table shows how much data Gordon uses each week before his next billing cycle. WEEK. DATA USAGE (IN GB) 1. 0.8 2. 1.3 3. 0.9 4. 1.1How much data does Gordon have left to roll over to the next billing cycle at the end of the four weeks?A. 0 GB of dataB. 0.8 GB of datac. 3 GB of data
Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.
What is Addition?
The sum of all the numbers are called the Addition of numbers.
Given that;
Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.
And, The table shows how much data Gordon uses each week before his next billing cycle as;
WEEK = 1 2 3 4
DATA USAGE = 0.8 1.3 0.9 1.1
Now,
Since, Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.
And, The table shows how much data Gordon uses each week before his next billing cycle.
So, We can add all the given data usage in 1 to 4 week as;
Data usage = 0.8 + 1.3 + 0.9 + 1.1
= 4.1 GB
Thus, Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.
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what is 3 to the negative 8th power divided by 3 to the negative 4th power
Answer
Answer = 3⁻⁴ = (1/3⁴) = (1/81)
The answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.
Explanation
The law of indices is usually applied when questions that involve same numbers with (different or the same) powers are considered.
When a number carrying a particular power is divided by the same number also carrying another power, the result is that same number raised to the power of the difference between the power of the numerator and the power of the denominator.
It'll be clearer in practice now.
[tex]\frac{3^{-8}}{3^{-4}}=3^{-8\text{ - (-4)}}=3^{-8+4}=3^{-4}[/tex]Hence, the answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.
Hope this Helps!!!
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
3. (02.04 MC)
Choose the equation that represents a line that passes through points (-6, 4) and (2, 0).
The answer to the question is here
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
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
A. Write an exponential function to model with population Y of bacteria X hours after 2 PM
B. How many bacteria were there at 7 PM that day
In this problem, we have an exponential growth function of the form
[tex]y=a(b)^x[/tex]where
a=10 bacteria (initial value at 2 pm)
b is the base of the exponential function
[tex]y=10(b)^x[/tex]Find out the value of b
we know that
For x=0 (2 pm), y=10 bacteria
At 5 pm
y=33,750 bacteria
x=(5 pm-2 pm)=3 hours
substitute in the exponential equation
[tex]33,750=10(b)^3[/tex]Solve for b
[tex]b^3=\frac{33,750}{10}[/tex][tex]\begin{gathered} b=\sqrt[3]{\frac{33,750}{10}} \\ b=15 \end{gathered}[/tex]the equation is
[tex]y=10(15)^x[/tex]Part B
At 7 pm
x=(7 pm-2 pm)=5 hours
substitute
[tex]\begin{gathered} y=10(15)^5 \\ y=7,593,750\text{ bacteria} \end{gathered}[/tex]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%.
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]What is the measure of EDH?EHFO 10°O 40°50°90
To find the measure of angle EDH we must solve for x first. Formulating an equation to find x, we have:
5x + 4x= 90 (Given that the sum of the angles EDH and HDG is equal to 90°)
9x = 90 (Adding like terms)
x= 90/9 (Dividing on both sides of the equation by 9)
x= 10
Replacing in the expression for angle EDH, we have:
m∠EDH = 5*(x) = 5*(10) = 50° (Multiplying)
The answer is m∠EDH =50°.
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)
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.
4. Which of the following represent the distance
formula? Select all that apply.
A d = √(x₁-x₂)² + (y₁ − y₂)²
B d = √(x₂− ×₂)² + (⁄₂ − y,}²
C d = √(x₂+x₂)² + (y₂ + y,)²
D d=√√₂-X₁1² + VY₂ − Y₁1²
A appears to be the only correct answer
a^2+b^2=c^2
you are solving for c when finding distance, so (a^2 + b^2) must be square rooted, as a whole, not separately
and a = (x1-x2)
and b = (y1-y2)
you can flip the 1 and 2 but you have to flip for both x and y
like x1-x2 means you have to do y1-y2
like x2-x1 means you have to do y2-y1
so both above are correct as long as the order of 1 and 2 stays the same for both x and y
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!!!
a teacher asks 15 students to estimate an answer to a question the answers or 1, 5, 5, 6, 7, 8, 10, 12 the correct estimate is 7 the teacher wants to calculate how far of the estimate were by finding the absolute value of the difference between each estimate and the answer which estimate was off by the most
We have the following estimations:
1, 5, 5, 6, 7, 8, 10, 12
The absolute value between each estimate and the answer is calculated as:
Estimate Absolute
Answer value
1 |1-7| = |-6| = 6
5 |5-7| = |-2| = 2
5 |5-7| = |-2| = 2
6 |6-7| = |-1| = 1
7 |7-7| = |0| = 0
8 |8-7| = |1| = 1
10 |10-7| = |3| = 3
12 |12-7| = |5| = 5
So, the estimated answer that was off by the most is 1.
What is the area of the circle to the nearest 10th unit?
First, lets find the radius of the circle.
For a circle inscribed in a square, the diameter of this circle is equal to the side lenght.
D = 4.4
Since the radius (r) is D/2
r = 4.4/2 = 2.2
Now, we can calcule the area of the circle (A), using the following equation:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot2.2^2 \\ A=4.8\pi units^2 \\ Or,\text{ since }\pi=3.14 \\ A=4.8\cdot3.14 \\ A=15.2\text{ }units^2 \end{gathered}[/tex]The bike you have been saving for is discounted 25%. You have $400 saved to purchase it. The original, non-discounted price of the bike is $450. There is a 5.44% sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax, how much money will you have left over? Round your answer to the nearest dollar.
1) Let's begin considering that our budget is $400.
Since the bike is discounted by 25%, we can get to know the price with this formula:
[tex]400\times(1-0.25)=\$300[/tex]2) Note that there is an increase in the price since there are taxes to pay. The original price is taken into consideration to charge the tax. So, let's find how much we have to pay:
[tex]450\times0.0544=\$24.48[/tex]So, let's add that to the discounted price:
[tex]\$300+\$24.48=\$324.48[/tex]3) Since I've got $400 let's find how much is left after that purchase:
[tex]\$400-\$324.48=\$75.52\approx\$76[/tex]Note that as requested we rounded off to the nearest dollar.
Thus, that's what's left after the purchase
Choose which function is represented by the graph.111032-11-10 9 8 7 6 5 4-3-2-102 3 4 5 6 7 8 9 10 1110O A. 1(x) = (x − 1)(x +2)(x+4)(x+8)B. f(x) - (x-8)(x-4)(x-2)(x+1)C. f(x)=(x-1)(x+2)(x+4)D. f(x)=(x-4)(x-2)(x+1)876544 4 4 & & To-2X
The factors of a polynomial tell us the points where the graph intersects the x-axis.
From the graph provided in the question, the graph cuts the x-axis at the points:
[tex]x=-4,x=-2,x=1[/tex]Therefore, the factors will be:
[tex]\begin{gathered} x=-4,x+4=0 \\ x=-2,x+2=0 \\ x=1,x-1=0 \\ \therefore \\ factors\Rightarrow(x+4),(x+2),(x-1) \end{gathered}[/tex]Therefore, the polynomial will be:
[tex]f(x)=(x+4)(x+2)(x-1)[/tex]OPTION C is the correct option.
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.
If the diameter of a quarter is 24.26 mm and the width of each quarter is 1.75 mm, to the nearest tenth, what is the approximate surface areaof the roll of quarters? Hint there are 40 quarters in a roll of quarters.A)14,366,2 mm
For this problem, we are given the dimensions of a quarter and we need to determine the surface area of a roll of quarters.
We can approximate the roll as a cylinder, where the height is the sum of the heights of all the quarters and the dimater is equal to the diameter of one quarter. Therefore we have:
[tex]\begin{gathered} A_{base}=\pi r^2=\pi(\frac{24.26}{2})^2=462.24\text{ mm^^b2}\\ \\ h=40\cdot1.75=70\text{ mm}\\ \\ L_{base}=2\pi(\frac{24.26}{2})=76.22\text{ mm}\\ \\ A_{lateral}=70\cdot76.22=5335.4\text{ mm^^b2}\\ \\ A_{surface}=2\cdot462.24+5335.4=6259.88\text{ mm^^b2} \end{gathered}[/tex]The surface area is equal to 6259.88 mm, the correct option is C.
f(x)A6X-868Which of the given functions could this graph represent?OA. f(t) = (x - 1)(x - 2)(x + 1)(x + 2)O B. f(x) = x(x - 1)(1 + 1)Oc. /(x) = x(x - 1)(x - 2)(x + 1)(x + 2)OD. (r) = x(x - 1)(x - 2)
The Solution:
Given the graph below:
We are required to determine the function that best describes the above graph.
Step1:
Identify the roots of the function from the given graph.
[tex]\begin{gathered} x=-2 \\ x=-1 \\ x=1 \\ x=2 \end{gathered}[/tex]This means that:
[tex]\begin{gathered} x+2=0 \\ x+1=0 \\ x-1=0 \\ x-2=0 \end{gathered}[/tex]So, the required function becomes:
[tex]f(x)=(x-1)(x-2)(x+1)(x+2)[/tex]Therefore, the correct answer is [option A]
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
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}
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)ihow 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.
hello I just need help with these no need to explain just the answers please
The two pairs of angles are supplementary
Here, we want to complete the given sentence
We want to find the relationship between two parallel lines which are cut by a transversal
A figure showing the described relationship is given below;
Now, we want to find the relationship between the two marked angles
From what we have, the two marked angles are supplementary
What this mean is that both angles add up to 180 degrees
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
I need help with thisIt asks to graph the functionIf you can, use Desmos to graph
Given the function
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]The graph of the function is dhoe below
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
