we make an expression
[tex]12\times x=17[/tex]we know that if we multiply to twelve by the ratio of increase we will obtain 17
now solve for x that is the ratio
[tex]x=\frac{17}{12}=1.42[/tex]multiply by 100 to obtain a percentage
[tex]1.42\times100=142[/tex]the percentage is 142%
Determine whether the arc is a minor arc, a major arc, or a semicircle of R. Questions 25 nd 27
We can find the missing angles using the drawing below.
Then,
[tex]\begin{gathered} 360=60+60+55+x+y \\ \text{and} \\ 55+y=x \\ \Rightarrow240=2(55+y) \\ \Rightarrow120=55+y \\ \Rightarrow y=65 \\ \Rightarrow x=120 \end{gathered}[/tex]Therefore
25)
Arc JML covers an angle equal to 65+55+60=180; thus, ArcJML is a semicircle of R.
27)
Which of the following is the explicit formula for a compound interestgeometric sequence?
INFORMATION:
We have the following options
And we must select the one that represents the explicit formula for a compound interest geometric sequence
STEP BY STEP EXPLANATION:
To select the correct one, we need to know that:
[tex]P_n=P_1(1+i)^{(n-1)}[/tex]Finally, the correct one would be option A
ANSWER:
[tex]A.\text{ }P_n=P_1\cdot(1+i)^{n-1}[/tex]What is the product of 0.976 and 1.2
At the fast food restaurant, an order of fries costs $0.94 and a drink costs $1.04. Howmuch would it cost to get 3 orders of fries and 2 drinks? How much would it cost toget f orders of fries and d drinks?
Determine the total cost for 3 order of fries and 2 drinks.
[tex]\begin{gathered} T=3\cdot0.94+2\cdot1.04 \\ =2.82+2.08 \\ =4.9 \end{gathered}[/tex]Determine the expression for f orders of fries and d drinks.
[tex]\begin{gathered} T=f\cdot0.94+d\cdot1.04 \\ =0.94f+1.04d \end{gathered}[/tex]So cost of 3 order of fries and 2 drinks is $4.9.
The cost order for f orders of fries and d drinks is 0.94f + 1.04d.
Find the area and the circumference (or perimeter) of each of the following. (a)a penny; (b) anickel; (c) a dime; (d) a quarter, (e) a half-dollar; (f) a silver dollar; (g) a Sacajawea dollar; (h) adollar bill; and (i) one face of the pyramid on the back of a $1 bill.
You use this for the coins
Area of a circle:
[tex]A=\pi\cdot r^2[/tex]r is the radius and it can be obtaided more easily if you measure the diameter of the circle and then divide it into 2.
Circunference or perimeter of a circle:
[tex]C=2\cdot\pi\cdot r[/tex]--------------------------------------------
You use this for the bills:
Aera of a rectangle:
[tex]A=l\cdot w[/tex]Perimeter of a rectangle:
[tex]P=2l+2w[/tex]------------------------
The face a pyramid has the shape of a trianlge:
Area of a triangle:
[tex]A=\frac{1}{2}b\cdot h[/tex]Perimeter of a triangle:
[tex]P=b+a+a[/tex]A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings
below:
Pepperoni
Sausage
Chicken Green pepper
Mushroom Pineapple
Ham
Onion
Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is
going to randomly choose 2 different toppings.
What is the probability that Rosa's mom chooses sausage and onion?
Choose 1 answer:
The Probability that Rosa's mom chooses sausage and onion is [tex]\frac{1}{^{8} C_{2} }[/tex]
What is Probability?Probability is the likelihood of an event occurring, measured by the ratio of the favorable cases to the whole number of cases possible.
The probability of an event happening = number of possible outcomes/total number of outcomes.
The number of possible outcomes is 8 exactly 1 of the total possible groups of toppings is sausage and onion.
The total number of outcome is 8 ways, because she has to choose the 2 toppings from possible 8 toppings
So the probability that Rosa's mom will chooses sausage and onion is [tex]\frac{1}{^{8} C_{2} }[/tex]
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An airplane takes off from an airport that is 144 ft above sea level. The airplane flies at 30,000 ft. To avoid a storm , the airplane goes up to 35,000 ft. Immediately after passing the storm, the airplane returns to its original altitude. Finally , the airplane lands at an airport that is 1,998 ft above sea level . What integer represents the airplanes changes in altitude to avoid the storm ? Immediately after passing the storm ? the integer □ represents the change in altitude to feet to avoid the storm.the integer □ represents the change in altitude in feet immediately after passing the storm.
What integer represents the airplanes changes in altitude to avoid the storm ?
changes = 35000 - 30000
= 5000 ft
the integer 5000 represents the change in altitude to feet to avoid the storm.
the integer -5000 represents the change in altitude in feet immediately after passing the storm.
A 4-pound bag of potatoes costs $3.96. What is the unit price?
Given that 4-pound bag of potatoes costs $3.96 then the unit price which is same as the cost of a pound
= $3.96/4
= $0.99
The unit price is $0.99
A basketball player shooting from the foul line has a 40% chance of getting a basket. He takes five shots. Whether he scores on one shot is independent of what he does on another shot. What is the probability that he misses at most one basket (rounded off to three decimals)?
The probability that the basketball player misses at most one basket is 0.077 as it is a mutually exclusive event.
what are mutually exclusive events in probability?Two events are said to be mutually exclusive if they cannot occur at the same time or simultaneously. This implies they are disjoint events and the probability of both events occurring at the same time will be zero.
Let us represent the probability of the player getting a basket to be p(y) and that of not getting a basket to be p(x)
then p(y)=40%=40/100=2/5
p(x)=1-(2/5)=3/5
The probability the player misses at most one basket implies his highest miss is one out of the five shots he took
So, the probability that he missed the:
1st shot= (3/5)×(2/5)×(2/5)×(2/5)×(2/5)=48/3125
2nd shot= (2/5)×(3/5)×(2/5)×(2/5)×(2/5)=48/3125
3rd shot= (2/5)×(2/5)×(3/5)×(2/5)×(2/5)=48/3125
4th shot= (2/5)×(2/5)×(2/5)×(3/5)×(2/5)=48/3125
5th shot= (2/5)×(2/5)×(2/5)×(2/5)×(3/5)=48/3125
The probability that he misses at most one basket= (48/3125)+(48/3125)+(48/3125)+(48/3125)+(48/3125)+(48/3125)= 249/3125=0.0768.
Finally, from the workings the probability that the player misses at most one basket is 0.077 rounded up to three decimals
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A website recorded the number of referrals it received from social media websites over a 10-year period. The results can be modeled by g = 2500(150), where is the year and SSRinterpret the values of a and & in this situation.a represents the number of referrals after 9 years, represents the growth factor of the number of referrals each yeara represents the number of referrals it received at the start of the model; &represents the decay factor of the number of referralsa represents the number of referrals after 9 years; b represents the decay factor of the number of referrals sach yeara represents the number of referrals it received at the start of the model & represents the growth factor of the number offWhat is the annual percent increase?The annual percent increase is %.
Given
[tex]y=2500(1.50)^t[/tex]Find
Interpret the values of a and b , also annual percent increase
Explanation
As the general form of growth exponential function is in the form of
[tex]\begin{gathered} y=ab^t \\ \end{gathered}[/tex]where a is the inital value
t is the time
b= 1+r = where r is the rate of growth
so , in given situation
a represents the number of referrals it received at the start of the model; and b represents the growth factor of the number of referrals
option 4 is the correct one.
now we have to find the annual percent increase
for this we have to find the final referrels after 1 years.
for this put t = 2in given equation
[tex]\begin{gathered} y=2500(1.50)^2 \\ y=5625 \end{gathered}[/tex]annual percent increase =
[tex]\begin{gathered} \frac{5625-2500}{2500}\times100 \\ \\ \frac{3125}{2500}\times100 \\ \\ 125\% \end{gathered}[/tex]Final Answer
Therefore , the correct option is d .
the annual percent increase is 125%
PLEASE HELP I WILL GIVE BRAINLYEST!! ALGEBRA 1 HW
start at 4 on the positive y axis, then go up 3 and 5 to the left
Subtract the following polynomial. Once simplified, name the resulting polynomial. 5.) (10x² + 8x - 7) - (6x^2 + 4x + 5)
The given polynomial expression: (10x² + 8x - 7) - (6x^2 + 4x + 5)
[tex]\begin{gathered} (10x^2+8x-7)-(6x^2+4x+5) \\ \text{Open the brackets:} \\ (10x^2+8x-7)-(6x^2+4x+5)=10x^2+8x-7-6x^2-4x-5 \\ \text{Arrange the like term together:} \\ (10x^2+8x-7)-(6x^2+4x+5)=10x^2-6x^2+8x-4x-7-5 \\ \text{Simplify the like terms together:} \\ (10x^2+8x-7)-(6x^2+4x+5)=4x^2+4x-12 \end{gathered}[/tex]The resulting polynomial be:
[tex](10x^2+8x-7)-(6x^2+4x+5)=4x^2+4x-12[/tex]The highest degree of the polynomial is 2 so, the polynomial is Quadratic polynomial
Answer: 4x^2 + 4x - 12, Quadratic polynomial
an employee at the bank notices an abandoned account with a balance of $360. the bank charges a monthly fee of $8 to maintain an account. the equation for this situation is y = 360 - 8x, where x is the number of months, and y is the balance in dollars. Part A: Find the y-intercept Part B: Find the x-interceptPart C: Interpret the meaning of the x- and y-intercept in terms of the problem.
Given:
There are given the equation:
[tex]y=360-8x[/tex]Explanation:
(A):
To find the y-intercept, we need to put 0 for x and solve the equation for the value of y.
So,
From the function:
[tex]\begin{gathered} y=360-8(0) \\ y=360 \end{gathered}[/tex]Hence, the y-intercept is shown below:
[tex](0,360)[/tex](B):
To find the x-intercept, we need to put 0 for y and find the values for x:
So,
[tex]\begin{gathered} y=360-8x \\ 0=360-8x \\ 8x=360 \\ x=\frac{360}{8} \\ x=45 \end{gathered}[/tex]Hence, the value x-intercept is shown below:
[tex](45,0)[/tex](C):
The interpret the meaning of the x- and the y-intercept is shown below:
In the given context, the y-intercept, and x-intercept, mean x = 0 and y = 0 and also refers to the starting values.
For a time-based exercise, this will be the value when we started talking we read or when we started tracking the time and its related changes.
Use synthetic division to find the quotient and remainder when2x^3+ 9x^2- 8x+ 4 is divided by x - 2
Solution:
Given;
[tex]\frac{2x^3+9x^2-8x+4}{x-2}[/tex]Using Synthetic division;
Thus, the solution is;
[tex]\frac{2x^{3}+9x^{2}-8x+4}{x-2}=2x^2+13x+18+\frac{40}{x-2}[/tex]The quotient is;
[tex]2x^2+13x+18[/tex]The remainder is;
[tex]18[/tex]Mary is x years old. How old will she be in 10 years? How old was she 2 years ago?
We know that Mary is x years old.
The age in 10 years will be x plus 10, as follows:
[tex]M_{\text{age}+10}=x+10[/tex]And the age she had two years ago was:
[tex]M_{\text{age}-2}=x-2[/tex]An example of this could be: imagine that Mary is 10 years now. In ten years, she will have:
10 + 10 = 20 years ( we add 10 to the original number). Likewise, 2 years ago, she had 10-2 = 8 years.
Therefore, the answers are two equations:
[tex]M_{age+10}=x+10[/tex][tex]M_{\text{age}-2}=x-2[/tex]Braden goes to the store to buy earmuffs. The sign says they were originally $13.50 but they are on sale for 15% off. What is the cost of the earmuffs now
Answer:
$11.48
Step-by-step explanation:
Change 15% to 0.15. then you multiply 13.50 by 0.15
13.50 x 0.15 = 2.025
Then you round 2.025
by rounding 2.025 you should get 2.03
with that you should subtract $13.50 by 2.03
13.50 - 2.03 = 11.48
I hope this helps :)
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.
A graph with a line running through coordinates (-4, -6) and coordinates (2, 6)
Answer:
12/6 or 1/2
Step-by-step explanation:
you just plug the coordinates into demos calculator and then look at rise over run.
(9 •10^9)•(2•10)^-3)
First, let's distribute the exponent -3 for 2 and ten, like this:
[tex]\begin{gathered} 9\times10^9\times(2\times10)^{-3}^{} \\ 9\times10^9\times2^{-3}\times10^{-3} \end{gathered}[/tex]Now, we can apply the next property when we have a number raised to a negative power:
[tex]a^{-b}=\frac{1}{a^b}[/tex]Then:
[tex]\begin{gathered} 9\times10^9\times2^{-3}\times\frac{1}{10^3} \\ 9\times2^{-3}\times\frac{10^9}{10^3} \end{gathered}[/tex]And when we have a division of the same number raised to different powers we can apply:
[tex]\frac{a^b}{a^c}=a^{b-c}[/tex]then:
[tex]\begin{gathered} 9\times2^{-3}\times\frac{10^9}{10^3} \\ 9\times2^{-3}\times10^{9-3} \\ 9\times2^{-3}\times10^6 \\ 9\times\frac{1}{2^3}^{}\times10^6 \end{gathered}[/tex]Now, as we know, having 10 raised to 6 means that we are multiplying ten by ten 6 times, when we do this we get:
[tex]10\times10\times10\times10\times10\times10=1000000[/tex]And with 2 raised to three we get:
[tex]2\times2\times2=8[/tex]Then we have:
[tex]\begin{gathered} 9\times\frac{1}{8^{}}^{}\times1000000 \\ \frac{9\times1000000}{8^{}}^{} \\ \frac{9000000}{8^{}}^{} \\ \frac{4500000}{4}^{}=11250000 \end{gathered}[/tex]what is the domain and range of arccosine?Thanks!
Solution:
What is the domain and range of arccosine?
The function is
[tex]f(x)=\cos^{-1}(x)[/tex]The graph of the function is shown below
From the graph above;
The domain of the function is
[tex]-1\leq x\leq1[/tex]The range of the function is
[tex]0\leq y\leq\pi[/tex]Express y in terms of x. Then find the value of y when x= -1-3 (x + 2) = 5yY in terms of x:Y=
LEt's express y in term of x:
[tex]\begin{gathered} -3(x+2)=5y \\ y=\frac{-3(x+2)}{5} \end{gathered}[/tex]Therefore:
[tex]y=-\frac{3}{5}x-\frac{6}{5}[/tex]Now, if x=-1, then we have:
[tex]\begin{gathered} y=-\frac{3}{5}(-1)-\frac{6}{5} \\ =\frac{3}{5}-\frac{6}{5} \\ =-\frac{1}{5} \end{gathered}[/tex]Therefore, if x=-1 then y=-1/5
6. Find the distance from A to B for the hexagonal nut shown below: А 1.50 in BYo I've asked tutors and they have been unable to answer, after all it's only given one side and I need some help.
Let
x ------> the length side of the regular polygon
we have a regular hexagon
that means
the interior angle of this polygon is
180(6-2)/6=120 degrees
A regular hexagon can be divided into 6 congruent equilateral triangles
see the attached figure to better understand the problem
in the right triangle of the figure
we have that
sin(60)=0.75/x
solve for x
x=0.75/sin(60)
Remember that
[tex]\sin (60^o)=\frac{\sqrt[]{3}}{2}[/tex]substitute
[tex]\begin{gathered} x=0.75\colon\frac{\sqrt[]{3}}{2} \\ \\ x=\frac{1.50}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{1.50\sqrt[]{3}}{3}=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Part 2
Find the distance AB
Applying the Pythagorean Theorem
AB^2=1.5^2+x^2
substitute the value of x
AB^2=2.25+(3/4)
AB^2=3
[tex]AB=\sqrt[]{3}\text{ in}[/tex]the distance AB is the square root of 3 inches5. Monty compared the minimum of the function f(x) = 2x2 - x + 6 to theminimum of the quadratic function that fits the values in the table below.X-3-2-101g(x)0-5-6-34What is the horizontal distance between the minimums of the twofunctions?A 0.25B. 1C. 1.5D. 12
The function f is given by:
[tex]\begin{gathered} f(x)=2x^2-x+6 \\ \text{ Rewrite the quadratic function in vertex form} \\ f(x)=2(x^2-\frac{1}{2}x)+6 \\ =2((x-\frac{1}{4})^2-(-\frac{1}{4})^2)+6 \\ =2(x-\frac{1}{4})^2-2(\frac{1}{16})+6 \\ =2(x-\frac{1}{4})^2+\frac{47}{8} \end{gathered}[/tex]If a quadratic function is written in the form:
[tex]\begin{gathered} a(x-h)^2+k \\ where: \\ a>0 \end{gathered}[/tex]Then the function has a minimum point at (h,k)
And the minimum is k
In this case,
[tex]\begin{gathered} a=2\gt0 \\ h=\frac{1}{4}=0.25 \\ k=\frac{47}{8}=5.875 \end{gathered}[/tex]Therefore, the minimum of the function f is at (0.25, 5.875)
The minimum of the function given by the table is at (-1, -6).
Therefore, the required horizontal distance is given by:
[tex]0.25-(-1)=1.25[/tex]Therefore, the horizontal distance is 1.25
Pats normal pulse rate is 80 beats minute. How many times does it beat in 3/4 of a minute?
The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given,
Pat's normal pulse rate is 80 beats per minute.
So, 80 beats → 1 minute
Multiply both sides by 3/4
80 × 3/4 beats → 1 × 3/4 minute
(3/4) minute → 60 beats.
Hence "The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times".
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Area of a rectangle: A Solve for) Find l when A= 24 ft and u
The area of the rectangle is 24 ft^2
the width of the rectangle is w = 8 ft
The expression for the area of the rectangle is given as follows.
A = l * w
[tex]\begin{gathered} 24=l\times8 \\ l=\frac{24}{8}=3 \end{gathered}[/tex]The length is l = 3 ft.
[tex]l=\text{ 3 ft}[/tex]explain two ways to evulate 32(16-6)
There are two ways to evaluate the expression:
32(16 - 6)
WAY 1
Evaluate the expression in the bracket first, then multiply the result by the content outside the bracket.
32(10)
= 320
WAY 2
Remove the bracket straight, without simplifying the content inside the bracket by multiplying 32 by each element in the bracket.
32*16 - 32*6
= 512 - 192
= 320
And those are the two ways.
In △ABC, m∠A=45°. The altitude divides side AB into two parts of 20 and 21 units. Find BC.
The length of BC is 29 units (solved using trigonometry and its applications).
What is trigonometry?
Trigonometry (from Ancient Greek v (trgnon) 'triangle' and (métron)'measure') is a field of mathematics that explores the correlations between triangle side lengths and angles. The topic arose in the Hellenistic civilization during the third century BC from geometric applications to astronomical research. The Greeks concentrated on chord computation, whereas Indian mathematicians established the first-known tables of values for trigonometric ratios (also known as trigonometric functions) such as sine. Trigonometry has been used throughout history in geodesy, surveying, celestial mechanics, and navigation. Trigonometry is well-known for its many identities. These trigonometric identities are frequently used to rewrite trigonometrical expressions with the goal of simplifying an expression, finding a more usable form of an expression, or solving an equation.
Let the point where AB is cut through line from C be D
This can be solved using trigonometry and its applications.
In triangle ACD,
tan 45° = CD/AD
or, CD = tan 45° x AD
= 1 x 20
= 20 units
In triangle CDB,
tan Ф = CD/BD
or, Ф = tan⁻¹(CD/BD)
= tan⁻¹(20/21)
= 43.6°
so, sin 43.6° = CD/BC
or, BC = CD/sin 43.6°
= 20/0.689
= 29 units
The length of BC is 29 units.
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Answer:
29
Step-by-step explanation:
BC is a side of ACB, which is a 45 45 90 triangle. BC = AB/SQRT2
I need help Options for the first box: -3, 1/3, 3, -1/3 Options for the second box -303, 363, 183, -60
To find the common ratio of the sequence, divide each of the elements of the sequence by the element that precedes it:
[tex]\begin{gathered} \frac{-9}{3}=-3 \\ \frac{27}{-9}=-3 \\ \frac{-81}{27}=-3 \end{gathered}[/tex]Since the quotient is always -3, then the common ratio is equal to -3.
To find the fifth term of the sequence, multiply the fourth term, which is -81, times -3:
[tex]-81\times-3=243[/tex]Once that we know the first five terms of the sequence, add them to find their sum:
[tex]\begin{gathered} 3-9+27-81+243 \\ =-6+27-81+243 \\ =21-81+243 \\ =-60+243 \\ =183 \end{gathered}[/tex]Therefore:
The common ratio of the sequence is -3.
The sum of the first five terms of the sequence is 183.
Which of the following sets of ordered pairs represents a function?
A.
{ (0, -2), (-27, -13), (-10, -5), (-27, -12) }
B.
{ (-7, -14), (-9, -18), (-5, -10), (-6, -12) }
C.
{ (1, -1), (1, -27), (1, -26), (1, -17) }
D.
{ (81, 1), (81, -1), (83, 4), (86, 6) }
Answer: B
Step-by-step explanation:
For the set of ordered pairs to be a function, each x-value has to correspond to only one y-value.
In option A, the x-value of -27 corresponds to both -13 and -12.
In option C, the x-value of 1 corresponds to -1, -27, -26, and -17.
In option D, the x-value of 81 corresponds to both 1 and -1.
7, -28, 112, -448, ..... as a formula
n = number
We can see that the value of each number is multiplied by 4 at each point in time
And the initial value is 7
[tex]a_n=7(4)^{n-1}[/tex]Match each expression with its translation.1. 3 na number increased by three2. a +3the quotient of three and a number3. Y-3three times a number4. 3 = xthree subtracted from a number
A number increased by three:
Every time we read a number, it's an unknown value represented with a letter (x,y, a,n)
increased by three means t
