Given:
Let x be the number of the cards and y be the number of the package.
Given that the number of cards is at least 4 more than twice the number of packages.
[tex]x=2y+4[/tex]Given that mailing costs no more than $500 and the cost of mailing a card is $3 and for a package, the cost is $7.
[tex]3x+7y=500[/tex]Substitute x=2y+4 in this equation, we get
[tex]3(2y+4)+7y=500[/tex][tex]6y+8+7y=500[/tex][tex]13y=500-8[/tex][tex]y=\frac{492}{13}[/tex][tex]y=37.8[/tex]Let y=37 and substitute in x=2y+4, we get
[tex]x=2\times37+4[/tex][tex]x=78[/tex]Hence the number of cards = 78 and the number of packages =37.
The total cost for this is $493 not more than $500.
If f(x) = 3x4 + 2x3 – X + 15,what would be the list ofpossible rational roots?a) + 1, 5, 1,3,5,15b) +1,3,5,15c) }, 1, 3, 5, 15d) 1, 2, 3, 6, 9, 18
The original cost of a laptop computer was x dollars. The expression 0.36x represents the value of the laptop today. choose two expressions that also represent the value of the laptop today. A. 1 - 0.64xB. x - 0.36xC. x - 0.64xD. x (1 - 0.36) E. x (1 - 0.64)
The initial price of the computer was $X.
The current price is $0.36X
Thus, the current value is X-0.36X.
By taking the common factor, this can also be expressed as:
X(1-0.36).
Hence, the two(2) expressions that represent the value of the laptop today are options B and option D.
they are 45 baseball points there's 14 basketball points football 21 points soccer 20 points what is the ratio of soccer to baseball and simplest form?
Given:
Number of baseball points = 45 points
Number of basketball points = 14 points
Number of football points = 21 points
number of soccer points = 20 points.
To find the ratio of soccer to baseball points, we have:
soccer : baseball = 20 : 45
in simplest form, divide both sides by 5 which is the Greatest Common Factor (GCF) of both numbers.
Thus, we have:
20÷5 : 45÷5 = 4:9
Therefore, the ratio of soccer to baseball in simplest form is = 4 : 9
ANSWER:
4 : 9
A colony of bacteria is growing exponentially according to the function below, where t is in hours. What will the approximate number of bacteria be after 7 hours?A.270B.1082C.635,818D.45,674
we have the exponential function
[tex]B(t)=4e^{0.8t}[/tex]For t=7 hours
substitute
[tex]\begin{gathered} B(t)=4e^{0.8*7} \\ \\ B(t)=1,082\text{ bacteria} \end{gathered}[/tex]The answer is option BHailey's hope his dad move their old television which weighed 81 lb to the basement then he helped set up their new 32-pound television in the family room how much more did the old television weigh then the new one
To find the answer to this question, find the difference between the old television weight and the new television weight. Substract 32 to 81:
[tex]81-32=49[/tex]The old television weighs 49 pounds more than the new one.
Martin is 6 years old when his sister Cassandra is 3 years old. How old will Martin be when Cassandra is 6 years old?
Explanation:
Martin's age = 6 years old
Casandra's age = 3 years old
Difference in their age = 6 - 3
Difference in their age = 3
Marissa can plant 10 seeds in 1/5 hour. she divides to find the number of seeds she can plant per hour but she makes a mistake
Marissa can plant 10 seeds in 1/5 hour
Then averagely, she will plant 1 seed in
[tex]undefined[/tex]You randomly draw a marble, put it back, and then randomly draw a marble.What is the probability of drawing a yellow marble and then drawing a green marble? Write answer as a fraction.
Given:
The total number of marbles =7.
The number of yellow marbles = 2.
The number of green marbles =2.
The marbles are replaced after being drawn.
To find:
We need to find the probability of drawing a yellow marble and then drawing a green marble.
Explanation:
The probability of drawing yellow marble P(Y).
[tex]P(Y)=\frac{The\text{ number of yellow marbles}}{The\text{ total number of marbles}}[/tex][tex]P(Y)=\frac{2}{7}[/tex]The probability of drawing green marble P(G).
[tex]P(G)=\frac{The\text{ number of gr}een\text{ marbles}}{The\text{ total number of marbles}}[/tex][tex]P(G)=\frac{2}{7}[/tex]The probability of drawing a yellow marble and then drawing a green marble is
[tex]=P(Y)\times P(G)[/tex][tex]=\frac{2}{7}\times\frac{2}{7}[/tex][tex]=\frac{4}{49}[/tex]Final answer:
The probability of drawing a yellow marble and then drawing a green marble is 4/49.
The regular price of a shirts is $12.00.If Jason bought the shirt for 45% off the regular price,how much did he save? A. $4.50 B. $5.40 C. $5.60 D.$6.60
First, we need to find 45% of $12
45% of $12 = 45/100 x12 = $5.4
He bought the shirt : $12 - $5.4 = $6.6
Therefore he saved $5.40
(a) Approximate the population mean and standard deviation of age for malesMale and female populations of totunder 10 years old are represented by age inthe table below. Completo port(a) through10(Round to two decimal places as needed)
Answer:
Step-by-step explanation:
The population means is an average of a group characteristic. A characteristic is just an item of interest.
[tex]\begin{gathered} \mu=\frac{\sum ^{}_{}x}{N} \\ \mu=\frac{\text{Sum of all the items}}{\text{ Number of items}} \end{gathered}[/tex]Then, for the population mean and standard deviation of the age for males;
Total of population: 266
[tex]undefined[/tex]The angle of elevation and the angle of depression are congruent because they areA)Corresponding AnglesB)Alternate Interior AnglesC)Alternate Exterior AnglesD)Vertical Angles
Given:
There are given the statement:
The angle of elevation and the angle of depression are congruent:
Explanation:
According to the concept:
The angle of elevation and the angle of depression are congruent because they belong from an alternate interior angle.
Final answer:
Hence, the correct option is B.
A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=15√t+2, find the area of the ripple as a function of time. Find the area of the ripple at t=2 .
FiThe radius, in inches, grows as a function of time in minutes according to:
[tex]r(t)=15\sqrt{t+2}[/tex]We know that the area of a circle is given by:
[tex]A=\pi r^2[/tex]Where r is the radius of the circle. Then, using r(t) in this equation:
[tex]\begin{gathered} A(t)=\pi\cdot\lbrack r(t)\rbrack^2=\pi\lbrack15\sqrt{t+2}\rbrack^2 \\ \\ \therefore A(t)=225\pi(t+2) \end{gathered}[/tex]Finally, we evaluate this function for t = 2:
[tex]\begin{gathered} A(2)=225\pi(2+2)=225\pi(4) \\ \\ \therefore A(2)=900\pi\text{ in}^2 \end{gathered}[/tex]I'm using goformative to do my work, I have number 13 answer right but the rest show my answers incorrect, I will appreciate if you can help me with my question I will paste the image of the question I have.
Firstly, we will have to make a representation of the angle
We have this as follows;
As we can see, alpha added to theta is 180 degrees
Firstly, by the use of Pythagoras' theorem, we can get the value of r
r faces the right angle, and that makes it the hypotenuse
According to the theorem, the square of r, the hypotenuse equals the sum of the squares of the two other sides
Thus, we have it that;
[tex]\begin{gathered} r^2=(-2)^2+4^2 \\ r^2\text{ = 4 + 16} \\ r^2\text{ = 20} \\ r\text{ = }\sqrt[]{20} \\ r\text{ = 2}\sqrt[]{5} \end{gathered}[/tex]From here, we can proceed to get the individual trigonometric ratios
a) Sine
This is the ratio of the opposite to the hypotenuse
On the second quadrant, the value of sine is positive
Thus, we have it that;
[tex]\begin{gathered} \sin \text{ }\alpha\text{ = }\frac{4}{2\sqrt[]{5}} \\ \alpha\text{ = }\sin ^{-1}(\frac{4}{2\sqrt[]{5}}) \\ \alpha\text{ = 63.43} \\ \theta\text{ = 180-63.43} \\ \theta\text{ = 116.57} \\ \sin \text{ 116.57 = }\frac{4}{2\sqrt[]{5}\text{ }}=\text{ }\frac{4\sqrt[]{5}}{10}\text{ = }\frac{2\sqrt[]{5}}{5} \\ \\ \sin \text{ }\theta\text{ = }\frac{2\sqrt[]{5}}{5} \end{gathered}[/tex]b) cosine
The cosine of an angle is the ratio of the adjacent to the hypotenuse
Mathematically, we know that;
[tex]\begin{gathered} \cos ^2\theta+sin^2\theta\text{ = 1} \\ \cos ^2\theta=1-sin^2\theta \\ \cos ^2\theta\text{ = 1 - (}\frac{2\sqrt[]{5}}{5})^2 \\ \\ \cos ^2\theta\text{ = 1- }\frac{20}{25} \\ \\ \cos ^2\theta\text{ = }\frac{5}{25} \\ \cos ^2\theta\text{ = }\frac{1}{5} \\ \\ \cos \text{ }\theta\text{ = }\sqrt[]{\frac{1}{5}} \\ \\ \cos \text{ }\theta\text{ = -}\frac{\sqrt[]{5}}{5} \end{gathered}[/tex]We choose the negative value for the cosine since cosine is negative on the second quadrant
c) Tan
The tan of an angle is the ratio of the opposite to the adjacent
Also, by dividing the sine of an angle by the cosine of the same angle, we can get the tan of the angle
Thus, we have it that;
[tex]\begin{gathered} \text{Tan }\theta\text{ = }\frac{\sin \text{ }\theta}{\cos \text{ }\theta} \\ \\ \text{Tan }\theta\text{ = }\frac{\frac{2\sqrt[]{5}}{5}}{\frac{-\sqrt[]{5}}{5}}\text{ = }\frac{2\sqrt[]{5}}{5}\times\frac{5}{-\sqrt[]{5}}\text{ = -2} \end{gathered}[/tex]d) cosec theta
The cosec of an angle is the multiplicative inverse of the sine
Mathematically;
[tex]\begin{gathered} co\sec \theta\text{ = }\frac{1}{\sin \text{ }\theta} \\ \\ co\sec \text{ }\theta\text{ = }\frac{1}{\frac{2\sqrt[]{5}}{5}}\text{ = }\frac{5}{2\sqrt[]{5}}\text{ = }\frac{5\sqrt[]{5}}{10}\text{ = }\frac{\sqrt[]{5}}{2} \end{gathered}[/tex]e) sec theta
The sec of an angle is the multiplicative inverse of the cosine of the angle
Thus, we have it that;
[tex]\text{sec }\theta\text{ = }\frac{1}{\cos \text{ }\theta}\text{ = }\frac{1}{-\frac{\sqrt[]{5}}{5}}\text{ = -}\frac{5}{\sqrt[]{5}}\text{ = -}\frac{5\sqrt[]{5}}{5}\text{ = -}\sqrt[]{5}[/tex]f) cot theta
The cot of an angle is the multiplicative angle of the tan
Thus, we have it that;
[tex]\begin{gathered} \cot \text{ }\theta\text{ = }\frac{1}{\tan \text{ }\theta} \\ \\ \cot \text{ }\theta\text{ = }\frac{1}{-2}\text{ = -}\frac{1}{2} \end{gathered}[/tex]Which parent function is f(x)=2^x?
Given the function:
[tex]f(x)=2^x[/tex]As the coefficeint of x = 1
So, the given function represents a parent function
The volume of a cylinder is 603.2 cubic inches. If the cylinder has a height of 12 inches, what is the area of the base
Volume of a cylinder = base area x heigth
Volume = 603.2 in3
Height = 12 in
Replacing:
603.2 = base area x 12
603.2/12 = base area
Base area = 50.26 in2
Bob works as a plumber he charges an initial fee of $45 and $32.50 an hour Bob was paid $207.50 for his last job how many hours did Bob work on his last job
We have the following:
Bob's earnings can be calculated with the following equation
[tex]B=45+32.5x[/tex]where x is the number of hours, they tell us that he made a profit of $ 207.50, we replace and solve for x
[tex]\begin{gathered} 207.5=45+32.5x \\ 32.5x=207.5-45 \\ x=\frac{162.5}{32.5} \\ x=5 \end{gathered}[/tex]Therefore, Bob worked a total of 5 hours
write a polynomial function of least degree with integral coefficients that had the given zeros. -3,3,-2
x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.
Given, the zeros of a polynomial be,
-3 , 3 and -2
As, the polynomial has 3 zeros then the degree of the polynomial is also be , 3.
Let the polynomial be,
p(x) = (x - (-3))(x - 3)(x - (-2))
p(x) = (x + 3)(x - 3)(x + 2)
On multiplying the factors, we get
p(x) = (x² - 3²)(x + 2)
p(x) = (x² - 9)(x + 2)
p(x) = (x³ - 9x + 2x² - 18)
p(x) = x³ + 2x² - 9x - 18
So, x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.
Hence, x³ + 2x² - 9x - 18 is the polynomial function of least degree with integral coefficients that had the zeros -3 , 3 , -2.
Learn more about Polynomials here https://brainly.com/question/23974386
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which shows the line of best fit for the data
Solution:
Given:
Graphs showing lines through different points.
To get the line of best fit for the data.
The line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
It is the line that touches most points or passes through most of the points.
From the four graphs given, the line that touches or passes through most points is;
Therefore, the graph above is the line of best fit.
The second graph is the correct answer.
In the diagram below of triangle NPQ, R is a midpoint of NP and S is a midpoint of PQ. If RS 15 - x, and NQ = 9x - 36, what is the measure of NQ?
The triangle midpoint theorem is as stated above.
In our case,
RS is joining the midpoints of NP and PQ.
Hence by the triangle midpoint theorem,
[tex]\begin{gathered} RS\parallel NQ\text{ and } \\ RS=\frac{1}{2}NQ \end{gathered}[/tex]Therefore,
triangle PRS is similar to triangle PNQ.
This means that the ratios of their corresponding sides are equal.
[tex]\frac{NQ}{RS}=\frac{NP}{RP}[/tex]Since R is the midpoint of NP then
[tex]\frac{NP}{RP}=2[/tex]Therefore,
[tex]\begin{gathered} \frac{NQ}{RS}=2 \\ \Rightarrow NQ=2RS \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 9x-36=2(15-x) \\ \Rightarrow9x-36=30-2x \\ \Rightarrow9x+2x=30+36 \\ \Rightarrow11x=66 \\ \Rightarrow x=\frac{66}{11}=6 \end{gathered}[/tex][tex]\begin{gathered} \text{ Therefore,} \\ NQ=9x-36 \\ \text{gives} \\ NQ=9(6)-36=54-36=18 \end{gathered}[/tex]Hence the measure of NQ is 18
anwsers a. x = 9; angle measure is 27°b. x = 9; angle measure is 45°c. x = 15; angle measure is 45°d. x = 15; angle measure is 27°
The sum of angle 3x and 45 is equal to 72. So equation for x is,
[tex]3x+45=72[/tex]Simplify the equation to obtain the value of x.
[tex]\begin{gathered} 3x+45=72 \\ 3x=72-45 \\ 3x=27 \\ x=9 \end{gathered}[/tex]Determine the measure of angle 3x.
[tex]\begin{gathered} 3x=3\cdot9 \\ =27 \end{gathered}[/tex]So value of x is 9 and measure of angle 3x is 27 degree.
Please help me answer question 1,2 and plot this graph
b: When x increases by 1, y increases 1 unit.
c. Apply the slope formula (m)
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]Replace with 2 points form the table:
For example:
Point 1 = (x1,y1)= (0,3)
Point 2= (x2,y2)= (1,4)
Replacing:
[tex]m=\frac{4-3}{1-0}=\frac{1}{1}=1[/tex]Slope = 1
It doesn't need to be written because x multiplied by 1 is equal to x.
Graph.
y=mx+b
y=x+3
Where :
b= y-intercept = 3( where the line crosses the y-axis)
m= slope=1
can you help me plot these points on the number line
To plot these numbers on the given umber line, we need to identify where they would be on the number line
The number 2 3/8 is between 2 and 3 while the number 1 3/4 is between the 1 and 2
Now, we need to identify each of the small points between the numbers
Between two numbers on the line, we can count 7 small lines and a total of 8 spaces
Now to get what each of the small lines represent, we need to divide 1 by the number of spaces.
What this mean is that each of this small numbers between each of the big digits represent the fraction 1/8
Now, recall, we know that 2 3/8 is between 2 and 3, to identify the exact place to position it, divide the fractional part by 1/8
What this mean is that we have 3/8 divided by 1/8 = 3/8 * 8/1 = 3
So what this means is that the number 2 3/8 is on the third small line after 2 (between 2 and 3)
For 1 3/4, we know that the number is between 3 and 4
To know thw exact spot, we find the division of the fractional part by 1/8
Mathematically, that will be 3/4 divided by 1/8 = 3/4 * 8/1 = 6
So this mean it is on the sixth small line after 1 (between 1 and 2)
A Type I error is the mistake of ________ when it is actually true. rejecting the null hypothesisA study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
Question 2
Answer:
Explanation:
Let x be a random variable representing the mean amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado. Given that it is normally distributed, we would calculate the z score by applying the formula,
z = (x - μ)/σ/√n
where
μ is the population mean
x is the sample mean
σ is the population standard deviation
n is the sample size
From the information given,
n = 40
x = 8.9
μ = 8.4
σ = 1.8
Thus,
z = (8.9 - 8.4)/(1.8/√40) = 1.76
We want to calculate P(x < 8.9). The probability value corresponding to z = 1.76 from the normal distribution table is 0.9608
Thus, the probability that their mean rebuild time is less than 8.9 hours is 0.9608
The diagonal of the figure Below represent the support beams for a patio covering.What IS the length of each support beam ? Given 30, and 10 yards
Since all the sides of the figure have the same length, then the figure is a rhombus. Then, its diagonals intersect at an angle of 90°.
Let O be the intersection of the diagonals of the rhombus. Notice that the triangle EOA is a right triangle. Since the side EA is the hypotenuse of the triangle, then, recalling the trigonometric functions:
[tex]\begin{gathered} \cos (30)=\frac{EO}{EA} \\ \sin (30)=\frac{OA}{EA} \end{gathered}[/tex]Use this information to solve for the segments EO and OA:
[tex]\begin{gathered} EO=EA\cdot\cos (30) \\ =10\cdot\frac{\sqrt[]{3}}{2} \\ =5\cdot\sqrt[]{3} \end{gathered}[/tex][tex]\begin{gathered} OA=EA\cdot\sin (30) \\ =10\cdot\frac{1}{2} \\ =5 \end{gathered}[/tex]Since the diagonal EM is twice the segment EO and the diagonal BA is twice the segment OA, then the lengths of the diagonals are:
[tex]\begin{gathered} BA=10 \\ EM=10\cdot\sqrt[]{3} \end{gathered}[/tex]Therefore, the answer is:
[tex]10\text{ yards and }10\cdot\sqrt[]{3}\text{ yards}[/tex]I am trying to graph a vertical shift for a greatest integer function
ANSWER
EXPLANATION
The graph of the parent function f(x) = [x] is
The function has the value of x until the next integer. So we have:
f(x) = 0 when x = 0 until x = 1, and then it changes to f(x) = 1. This is for all values of x. We can say that the function "jumps" on each integer and then keeps its value.
If we do a vertical shift of 2 units we have to add 2 to each value of the parent function. This way the shifted function is f(x) = 2 when x = 0 until x = 1, and then it jumps to f(x) = 3:
Two bags of flour have a total weight of834pounds. What could be their individual weights?Select all that apply.A.7pounds and34poundB.314pounds and512poundsC.434pounds and4poundsD.8pounds and14pound
Given:
Two bags have a total weight of 8 3/4 pounds.
What could be their individual weights?
To answer the question, we will select the option that gives a sum of 8 3/4
We will check the options:
A. 7 pounds and 3/4 pounds
The sum = 7 + 3/4 = 7 3/4 pounds
So, option A is wrong
B. 3 1/4 pounds and 5 1/2 pounds
The sum = 3 1/4 + 5 1/2 = 8 3/4
So, option B is correct
C. 4 3/4 pounds and 4 pounds
The sum = 4 3/4 + 4 pounds = 8 3/4 pounds
So, option C is correct
D. 8 pounds and 1/4 pounds
The sum = 8 + 1/4 = 8 1/4
So, option D is wrong
E. 6 pounds and 2 3/4 pounds
The sum = 8 3/4
So, E is correct
The answer will be: B and C and E
there are 30 votes for skating rink and 13 volts per bowling alley what is the ratio of number of votes for skating to the number of votes for bowling
Let's begin by listing out the given information:
Skating rink = 30 votes
Volts per bowling alley = 13
The ratio of the number of votes for skating to the number of votes for bowling is:
[tex]30\colon13[/tex]The function h(t) = -16t(t - 2) + 24 models the height h, in feet, of a ball t seconds after it is thrown straight up into the air. What are the initial velocity and the initial height of the ball? O 16 ft/s: 32 ft 32 ft/s: 24 ft 24 ft/s: 32 ft 48 ft/s: 24 ft
Answer
Option B is correct.
Initial velocity = 32 ft/s
Initial height = 24 ft.
Explanation
The function gives us the function that models the height, h, in feet for the ball as a function of time, t, in seconds.
h(t) = -16t (t - 2) + 24
We are then asked to find the initial velocity and the initial height of the ball.
This means we find the velocity and the height of the ball at t = 0
Velocity is given as the first derivative of the height function
v = (dh/dt)
h(t) = -16t (t - 2) + 24
h(t) = -16t² + 32t + 24
v = (dh/dt) = -32t + 32
When t = 0
v = -32t + 32 = -32 (0) + 32 = 0 + 32 = 32 ft/s
Initial velocity = 32 ft/s
For the initial height, t = 0
h(t) = -16t (t - 2) + 24
h(t) = -16t² + 32t + 24
h(0) = -16(0²) + 32(0) + 24
h(0) = 0 + 0 + 24
h(0) = 24 ft
Initial height = 24 ft.
Hope this Helps!!!
6 -7-6-5 4 5 6 기 7. I Which of these best represents the domain of f. F-3 5.5 ] All real numbers less than -3 or greater than 2
In this problem we have a quadratic function (vertical parabola open upward)
the domain is all real numbers
therefore
the answer is option GFirst to answer WILL get BRAINLIEST!
which equation is represented by this modal?
1/4 x 1/2 =1/8
1/3 x 1/2 =1/6
1/4 x 1/6 = 1/24
1/4 x 1/3 = 1/12
Answer:
1/4 x 1/2 =1/8
Step-by-step explanation:
The circle is split into four parts (1/4)
Then one of the parts is split in half (1/2)
So the equation represented by the model is 1/4 x 1/2 = 1/8
Answer:
1/4x1/2=1/8
Step-by-step explanation:
this is because it has 4 pieces and then it shows 1/2 of a 1/4 piece