Megan sent 792 text messages in the month of October .
In the question ,
it is given that
Cost for first 600 messages = $15
additional text message charge = $0.05
Amount owed by Megan for the month of October = $24.60
Let the number of Additional messages be x.
So, according to the question
15 + 0.05x = 24.60
0.05x = 24.60-15
0.05x = 9.6
x = 9.6/0.05
x = 192
number of extra messages = 192
total messages = first 600 messages + extra messages
= 600+192
= 792
Therefore , Megan sent 792 text messages in the month of October .
The given question is incomplete , the complete question is
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month ?
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Put the equation y = x2 - 10x + 16 into the form y = =(x - h)² + ki Answer: y = > Next Question
To complete the perfect square ((x-h)²) we add and subtract constants:
[tex]\begin{gathered} y=x^{2}-10x+16 \\ y=x^{2}-10x+25-25+16 \\ y=x^{2}-10x+5^{2}-9 \\ y=(x-5)^{2}-9 \end{gathered}[/tex]4. Identify the properties that are always true for the given quadrilateral by placing an X in the appropriate box. Property Parallelogram Rectangle Rhombus Square Isosceles Trapezoid Kite a. Opposite sides are parallel. b. Only one pair of opposite sides is parallel C. Opposite sides are congruent Side Relationships d. Only one pair of opposite sides is congruent e. All sides are congruent. f. 2 pairs of consecutive sides are congruent.
There is quadrilateral, means it has 4 lines
Is a rhombus
Find the real solutions of the equation by graphing. 4x^3-8x^2+4x=0
x = 0,1 are the real solutions of the equation .
What are real solutions in math?
Any equation's solution that is a real number is known as a "real solution" in algebra.Discriminant b2 - 4ac is equal to zero when there is only one real solution. One solution, x = -1, exists for the equation x2 + 2x + 1 = 0.There are a number of solutions to the given quadratic equation depending on whether the discriminant is positive, zero, or negative. The existence of two unique real number solutions to the quadratic is indicated by a positive discriminant. A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.4x³ - 8x² + 4x = 0
x( 4x² - 8x + 4 ) = 0
x( 4x² - 4x - 4x + 4 ) = 0
x ( 4x ( x - 1) -4 ( x - 1 )) = 0
x ( ( 4x - 4 ) ( x - 1 ) ) = 0
x = 0
4x - 4 = 0 ⇒ x = 1
x - 1 = 0 ⇒ x = 1
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13. Puppies have 28 teeth and most adult dogs have 42 teeth. Find the primefactorization of each number. Write the result using exponents. (Example 5)
To solve our question, first we need to know that a prime factorization is a way to represent a number by a sequence of prime numbers that multiplied together gives us the original number.
So let's calculate our first prime factorization:
As we can see, we divide our number by the smallest prime number and then the factor we follow the same rule until we get "1" (for all divisions we just have integers).
Now, for the second number we have:
And both prime factorizations are our final answers.
5)Which of the following is a critical number of the inequality x^2+5x-6<0 ?
Answer:
B. 1
Explanation:
Given the inequality:
[tex]x^2+5x-6<0[/tex]To find the critical number, first, change the inequality sign to the equality sign :
[tex]x^2+5x-6=0[/tex]Next, solve for x:
[tex]\begin{gathered} x^2+6x-x-6=0 \\ x(x+6)-1(x+6)=0 \\ (x-1)(x+6)=0 \\ x-1=0\text{ or }x+6=0 \\ x=1\text{ or }x=-6 \end{gathered}[/tex]Therefore, from the options, 1 is the critical number.
The correct option is B.
14 pointsWhich are the coefficients of the terms in the algebraic expression, x2 - 3x?O and -31 and -3O and 351 and 36
Answer:
The coefficients of the terms in the algebraic expression are 1 and -3
[tex]1\text{ }and-3[/tex]Explanation:
The coefficients are the number that multiplies an algebraic term in an algebraic expression.
for example; the coefficient of 3x is 3.
[tex]3x=3\times x[/tex]For the question;
given the expression;
[tex]x^2-3x[/tex]The coefficient of x^2 is 1
[tex]x^2=1\times x^2[/tex]while the coefficient of x is -3
[tex]-3x=-3\times x[/tex]Therefore, the coefficients of the terms in the algebraic expression are 1 and -3
[tex]1\text{ }and-3[/tex]h(x) = x2 + 1 k(x) = x-2 (h - k)(3) = DONE
We are given two functions:
h(x) = x^2 + 1
and k(x) = x - 2
We are asked to find the value of:
(h - k) (3) (the value of the difference of the two functions at the point x = 3
So we performe the difference of the two functions:
(h - k) (x) = x^2 + 1 - (x - 2) = x^2 + 1 - x + 2 = x^2 - x + 3
So, this expression evaluated at 3 gives:
(h-k)(3) = 3^2 - 3 + 3 = 9
One could also evaluate what was asked by evaluating each function independently and subtracting the results of such evaluation:
h(3) = 3^2 + 1 = 10
k(3) = 3 - 2 = 1
Then, the difference is : h(3) - k(3) = 10 - 1 = 9
So use whatever method feels more comfortable for you.
I need help with the problem!
a)The vertex of the function is (3, -1)
b)The line of symmetry is x= 3
c) The maximum is no maximum and minimum is (3, -1)
a) What is the vertex of the function of the parabola ?
[tex]f(x) = x^{2} -6x+8[/tex]
Transforming the function in the vertex form,
[tex]f(x) = a(x-h)^{2} +k[/tex]
[tex]f(x)=(x-3)^{2} -1[/tex]
The vertex of the function is given by,
(h, k) = (3, -1)
So ,the vertex of the function of the parabola is (3, -1)
b) What is the line of symmetry in the function?
In a parabola , the axis of symmetry is x = h.
Here, x = 3
So, the line of symmetry of the function of the parabola is x= 3
c) What is the maximum and minimum?
There is no maximum for the function because, the parabola opens upward. (Refer image for graph)The minimum for the function is the vertex (h, k) = (3, -1)What is a function of a parabola?
A parabola is the shape of a quadratic function's graph. Although the width or steepness of a parabola can vary as well as its direction of opening, they share the same fundamental U form. Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.To learn more about function of a parabola , refer:
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Calculate the probabilities of each of these situations. A standard deck of cards has 52 cards and 13 cards cards in each suit (Spades, Clubs, Hearts, & Diamonds). Which of the following is LEAST likely to occur? a) Selecting any spade card from a standard deck of cards, keeping it, then selecting the queen of hearts. b) Selecting a spade from a standard deck of cards, not putting it back, then selecting another spade. c) Selecting an ace from a standard deck of cards, not replacing it, then selecting a king.Event CEvent AEvent B
Answer
The least likely to occur is Event C
Explanation
A.
P(spade card) = 13/52
P(queen) = 4/51 Note: Without replacement
⇒ 13/52 x 4/51
= 52/2652
= 0.0196
B.
P(a spade) = 13/52
P( another spade) = 12/51 Note: Without replacement
⇒ 13/52 x 12/51
= 156/2652
= 0.0588
C.
P(an ace) = 4/52
P(king) = 4/51
⇒ 4/52 x 4/51
= 16/2652
= 0.006
∴ The least likely to occur is Event C
I got the first part I’m not sure of the 2nd is it 38.5
We will have the following:
The surface area of the onion can be best modeled by a sphere. Base on the model, the approximate area of the onion is 38.5 square inches:
[tex]A_s=4\pi(\frac{3.5}{2})^2\Rightarrow A_s\approx38.5[/tex]10. A $152,000 home has an assessment rate of 52% and a tax rateof $48 per $1,000. Use the effective tax method to calculate theproperty tax .Hint: When you determine the effective tax rate, round the rateto three places.
Given
$152,000
52% assessment rate
$48 per $1,000
Procedure
First, let's calculate the assessment rate.
[tex]152000\cdot0.52=79040.0[/tex]Now let's calculate the taxes
[tex]79040.0\cdot\frac{48}{1000}=3793.92[/tex]Property taxes are equal to $3,793.92.
what number need to be changed to make a linear function? And what does it have to turn into?
In order to have a linear function, the rate of change needs to be the same in each point
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For
(-18,2)=(x1,y1)
(-14,4)=(x2,y2)
[tex]m=\frac{4-2}{-14+18}=\frac{1}{2}[/tex]for
(-14,4)=(x1,y1)
(-12,5)=(x2,y2)
[tex]m=\frac{5-4}{-12+14}=\frac{1}{2}[/tex]for
(-12,5)=(x1,y1)
(0,12)=(x2,y2)
[tex]m=\frac{12-5}{0+12}=\frac{7}{12}[/tex]as we can see here are the two numbers so we will obtain the equation in order to know the number that needs to be change
[tex]y=\frac{1}{2}x+11[/tex]therefore if x=0
[tex]y=\frac{1}{2}(0)+11=11[/tex]the number we need to change is 12 and need to be changed for 11
(0,11)
a. The number that needs to be changed in order to create a linear function is 12
b. That number needs to be changed to 11 in order for the function to be linear
X+27+32 = 8
X+ 3y +32 = 10
X + 2y +42 = 9
Value of x and y are -51 and 8 respectively
What is Algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Let,
X+27+32 = 8
X+ 3y +32 = 10
X + 2y +42 = 9
Be, equation 1, 2 and 3 respectively
X+27+32 = 8 -----(1)
X+ 3y +32 = 10 -----(2)
X + 2y +42 = 9 -----(3)
From equation we can find the value of x
X+27+32 = 8
X + 59 = 8
X = 8 - 59
X = - 51
Substituting the value of x in equation 3
X + 2y +42 = 9
(-51) + 2y + 42 = 9
-51 + 42 + 2y = 9
-9 + 2y = 9
2y = 9 + 9
2y = 18
y = 18/2
y = 9
Hence, the value of x = -51 and y = 9
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Кр2.345 67 8Identify each angle as acute, obtuse, or right123345678.
we have the following:
Therefore:
how many km/h equals 880ft/min? Explain how you solved this problem
The number of kilometers per hour in 880 feet / minute can be found to be 16.09 kilometers per hour
How does km/h relate to ft/ min?Based on the conversion rates between kilometers and feet, the number of feet per minute for each kilometer per hour is 54.6807 feet per minute.
In other words, 1 km / h is equal to 54.6807 feet per minute.
If there are 880 ft / minute therefore, the number of kilometers per hour is:
= Speed in feet per minute / feet per minute per kilometer per hour
= 880 / 54.6807
= 16.09 kilometers per hour
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Choose the left side that makes a True statement, and shows at the sum of the given complex numbers is 10Choose the left side that makes a true statement, and shows that the product of the given complex numbers is 40
For statement one:
We need to add up to complex numbers and their sum must give us equal to 10.
Also, we need to use the complex numbers:
5+i√15 and 5-i√15.
Then, we can use:
(5+i√15)+( 5-i√15) =
5+i√15+5-i√15 =
5+5+ i√15-i√15 =
= 10 + 0
= 10
For the second statement:
We need to show the product of complex numbers:
Then, we use:
(5+i√15)(5-i√15))=
5*5 - 5*i√15) +5*i√15) +√15*√15=
25 + 0 + 15=
40
*You will use the following scenario forquestions 1-4*On the Wechsler Adult IntelligenceScale a mean IQ is 100 with a standarddeviation of 15. You may assume thatIQ scores follow a normal distribution.What percent of people have an IQscore less than 90?*Write your answer as a percent andround to 2 decimal places*
The Solution:
Given:
[tex]\begin{gathered} x=90 \\ \mu=100 \\ \sigma=15 \end{gathered}[/tex]By formula,
[tex]Z=\frac{x-\mu}{\sigma}=\frac{90-100}{15}=\frac{-10}{15}=-0.6667[/tex]From the z-score tables:
[tex]P(Z\leq90)=0.25248[/tex]Convert to percent by multiplying with 100.
[tex]0.25248\times100=25.248\approx25.25\text{\%}[/tex]Thus, the number of people that have an IQ score less than 90 is 25.25%
Therefore, the correct answer si 25.25%
Solve fort 30 on t =(Type (Type an integer or a simplified fraction)
Multiply both sides by t:
[tex]\frac{12t}{10}=30[/tex]Multiply both sides by 10:
[tex]12t=300[/tex]Divide both sides by 12:
[tex]\begin{gathered} t=\frac{300}{12} \\ t=25 \end{gathered}[/tex]Solve this system of equations by elimination. Enter your answer as an ordered pair (x,y). Do not use spaces in your answer. If your answer is no solution, type "no solution". If your answer is infinitely many solutions, type "infinitely many solutions".
5x + 2y = -12 (a)
3y + 5x =-8 (b)
First, write (b) in the ax+by=c form:
5x + 3y = -8 (b)
Now, subtract (b) to (a) to eliminate x
5x + 2y = -12
-
5x + 3y = -8
__________
-y = -4
solve for y:
Multiply both sides by -1
y=4
Replace y=4 on (a) and solve for x:
5x + 2 (4) = -12
5x + 8 = -12
5x = -12-8
5x = -20
x = -20/5
x = -4
Solution: (-4,4)
If $2,000 is invested at 6% compounded monthly, what is the amount after 5 years?
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is the number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$2,000
t=5 years
r=6%=6/100=0.06
n=12
substitute the given values in the above formula
[tex]\begin{gathered} A=2,000(1+\frac{0.06}{12})^{12*5} \\ \\ A=\$2,697.70 \end{gathered}[/tex]therefore
The answer is $2,697.70Use area under the curve to complete probability for continuous probability dentist functionsuse the uniform distribution to compute probabilityfind the mean and standard deviation Love the uniform distribution1.One type of card stock which may be used for the cover of a booklet is uncoated paper with waymark as 65 pounds the standard thickness of 65# of card stuck is 9.5 points (0.0095”). A manufacturer determines that the thickness of 65# of card stuck produced followed a uniform distribution varying between 9.25 points and 9.75 points.A)Sketch the description for this situation.B)compute the mean and standard division of the thickness of the 65# cards stuck producedC)compute the probability that a randomly selected piece of 65# card stark has a thickness of a list 9.4 points.D)Compute the probability that a randomly selected piece of 65# card stock has thickness between 9.75 points.
If x is uniformly distributed over the interval [ a , b ] then,
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{b-a}\text{ , a }\leq\text{ x }\leq\text{ b} \\ f(x)\text{ = 0 , otherwise} \end{gathered}[/tex]Also ,
[tex]\begin{gathered} \text{Mean = }\frac{a\text{ + b}}{2} \\ \text{Std deviation = }\sqrt[]{\frac{(b-a)^2}{12}} \end{gathered}[/tex]It is given that ,
[tex]\begin{gathered} a\text{ = 9.25} \\ b\text{ = 9.75} \\ b\text{ - a = 9.75 - 9.25 = 0.5} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} f(x)\text{ = }\frac{1}{0.5}\text{ 9.25 }\leq\text{ x }\leq\text{ 9.75} \\ f(x)\text{ = 0 otherwise} \end{gathered}[/tex](a)The distribution is as follows :
(b)The mean is calculated as,
[tex]\begin{gathered} \text{Mean = }\frac{a\text{ + b}}{2} \\ \text{Mean = }\frac{9.25\text{ + 9.75}}{2} \\ \text{Mean = 9.5} \end{gathered}[/tex]Standard deviation is calculated as,
[tex]\begin{gathered} \text{Standard deviation = }\sqrt[]{\frac{(b-a)^2}{12}} \\ \text{Standard deviation = }\sqrt[]{\frac{(0.5)^2}{12}} \\ \text{Standard deviation }\approx\text{ 0.1443} \end{gathered}[/tex](c) The probability is calculated as,
[tex]\begin{gathered} P(\text{ atleast 9.4 points ) = P( x }\ge\text{ 9.4)} \\ P(\text{ atleast 9.4 points ) = }\int ^{9.75}_{9.4}(\frac{1}{0.5})dx \\ P(\text{ atleast 9.4 points ) = }\frac{9.75\text{ - 9.4}}{0.5} \\ P(\text{ atleast 9.4 points ) = 0.7} \end{gathered}[/tex](d) The probability is calculated as,
[tex]\begin{gathered} P(\text{between 9.45 and }9.75\text{ ) = P( 9.45 }\leq\text{ x }\leq\text{ 9.75 )} \\ P(\text{between 9.45 and }9.75\text{ ) = }\int ^{9.75}_{9.45}(\frac{1}{0.5})dx \\ P(\text{between 9.45 and }9.75\text{ ) =}\frac{9.75\text{ - 9.45}}{0.5} \\ P(\text{between 9.45 and }9.75\text{ ) = 0.6} \end{gathered}[/tex]the remainder when f(x)is divided by x-3 is 15. Does f(-3) =15? explain why or why not
We will see that the function f(x) is:
f(x) = 15*(x - 3)
Evaluating it in x = -3 we can see that:
f(-3) = -90
Is the statement true?We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)
so we can write the equation:
f(x)/(x - 3) = 15
And we can solve this for f(x) as if it were a variable, then we get:
f(x) = 15*(x - 3)
Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:
f(-3) = 15*(-3 - 3) = 15*(-6) = -90
So the statement:
f(-3) = 15
Is false
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Find the present value that will grow to $6000 if the annual interest rate is 9.5% compounded quarterly for 9 yr.The present value is $(Round to the nearest cent as needed)
We need to know how to calculate compound interest to solve this problem. The present value is $2577.32
Compound interest is the interest that is earned on interest. Inorder to calculate the compound interest we need to know the principal amount, the rate of interest, the time period and how many times the interest is applied in per time period. In this question we know the amount after 9 years and the rate of interest is 9.5% and the interest is compounded quarterly. We will use the formula for compound interest get the principal value.
A=P[tex](1+\frac{r}{n}) ^{nt}[/tex]
where A= amount, P= principal, t=time period, n= number of times interest applied per time period, r=rate of interest
A=$6000
r=9.5%
t=9 yrs
n=4
6000=P[tex](1+\frac{9.5}{400} )^{36}[/tex]
6000= P x 2.328
P=6000/2.328=2577.32
Therefore the present value that will grow to $6000 in 9 years is $2577.32
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what would be the value if m in a angle on 50 degrees and 10m
50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.
10m = 90 - 50
10m = 40
m = 40/10
m = 4
30 randomly selected students took the statistics final. If the sample mean was 84, and the standard deviation was 12.2, construct a 99% confidence interval for the mean score of all students
The confidence interval for the mean score of the 30 randomly selected students is: 99% CI {78.26, 89.73}
What is confidence interval?Confidence interval is the range of values for which which is expected to have the values at a certain percentage of the times.
How to construct a 99% confidence intervalGiven data form the question
99% confidence interval
30 randomly selected students
mean sample = 84
Standard deviation = 12.2
Definition of variables
confidence level, CI = 99%
mean sample, X = 84
standard deviation, SD = 12.2
Z score, z = 2.576
from z table z score of 99%confidence interval = 2.576sample size, n = 30
The formula for the confidence interval is given by
[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex] OR [tex]CI=X-Z\frac{SD}{\sqrt{n} }[/tex]
[tex]=84+2.576\frac{12.2}{\sqrt{30} }[/tex]
=[tex]=84+2.576*2.2274[/tex]
= 84 + 5.7378 OR 84 - 5.7378
= 89.7378 OR 78.2622
= 89.73 to 78.26
The confidence interval for the mean score of all students is 78.26 to 89.78
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3. The sum of two consecutive odd integersis 168. What are the integers?
Integers are numbers such as
[tex]N=\text{ }.\ldots\text{-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9}\ldots.[/tex]And odd numbers are
[tex]1\text{ 3 5 7 9 11 13 }\ldots[/tex]need help asap look at attachment
Answer: Width =14, Length = 18
Step-by-step explanation:
L = W + 4
2W + 2L = 64
W+ L = 32
2W+ 4 = 32
2W = 28
W = 14
The expression secθ - ((tan^2)(θ)/(sec)(θ)) simplifies to what expression?−tan θ−cot θcos θsec θ
Given the expression
[tex]sec(\theta)-\frac{tan^2(\theta)}{sec(\theta)}[/tex]express in sen and cos terms
[tex]\frac{1}{cos(\theta)}-\frac{\frac{sin^2(\theta)}{cos^2(\theta)}}{\frac{1}{cos(\theta)}}[/tex][tex]\frac{1}{cos(\theta)}-\frac{sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{1-sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{cos^2(\theta)}{cos^(\theta)}[/tex][tex]cos^(\theta[/tex]then the correct answer is option C
Cos (angle)
g(x) = 2x - 5f(x) = 4x + 2Find g(f(x))
Explanation
Step 1
Let
[tex]\begin{gathered} g(x)=2x-5 \\ \text{and} \\ f(x)=4x+2 \end{gathered}[/tex]then
[tex]\begin{gathered} g(f(x))= \\ g(x)=2x-5 \\ g(f(x))=2(4x+2)-5 \\ \text{apply distributive property} \\ g(f(x))=8x+4-5 \\ g(f(x))=8x-1 \end{gathered}[/tex]I hope this helps you
an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?
The distance traveled by airplane is 180 miles.
The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°
The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.
Then, the total distance traveled by airplane will be:
= 100 miles + 80 miles = 180 miles.
The speed can be defined as the distance traveled by the total time taken.
Speed = distance/time
Speed = 180 miles/ 1 hour
Speed = 180 miles/60 minutes
Speed = 3 miles per minute
The angle of direction from its origin will be:
tan (x) = 100 miles/80 miles
x = tan⁻¹ ( 100/80)
x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)
x = 51.34°
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