The seniors decreased in 63 in 9 months. if the rate is the same for all the months, to know the monthly decrease we have to divide 63 by 9 and we get that
[tex]\frac{63}{9}=7[/tex]so the monthly decrease is 7
Decode please I need thing fast it will really help
Answer:
talcordkypher com
Step-by-step explanation:
just said the alphabet
point B divides pq in the ratio 1:3 if x cordinate is-1and the x corrdinate op is -3 what is the x cordinate of q
Help in example number two in the bottom right corner f(x) = -2x^2 - 8x + 1
First, find the vertex of the given function, we have
[tex]\begin{gathered} f(x)=-2x^2-8x+1 \\ \\ \text{The coefficients are } \\ a=-2,b=-8,c=1 \\ \\ \text{The x-coordinate of the vertex is at } \\ x=-\frac{b}{2a} \\ x=-\frac{-8}{2(-2)} \\ x=-\frac{-8}{-4} \\ x=-2 \end{gathered}[/tex]Next, substitute x = -2. to the given function and we get
[tex]\begin{gathered} f(x)=-2x^{2}-8x+1 \\ f(-2)=-2(-2)^2-8(-2)+1 \\ f(-2)=-2(4)+16+1 \\ f(-2)=-8+17 \\ f(-2)=9 \end{gathered}[/tex]Therefore, the vertex is at (-2.9).
The axis of symmetry is at x = -2.
The y-intercept at y = 1.
The x-intercepts are the following:
[tex]\begin{gathered} x=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a } \\ x = \frac{ -(-8) \pm \sqrt{(-8)^2 - 4(-2)(1)}}{ 2(-2) } \\ x=\frac{8\pm\sqrt{64-(-8)}}{-4} \\ x = \frac{ 8 \pm \sqrt{72}}{ -4 } \\ x = \frac{ 8 \pm 6\sqrt{2}\, }{ -4 } \\ \text{ Which becomes} \\ \\ x=\frac{8+6\sqrt{2}\,}{-4}\approx−4.12132 \\ x=\frac{8-6\sqrt{2}\,}{-4}\approx0.12132 \end{gathered}[/tex]Graphing the function we get
Mandy opened a savings account and deposited 100.00 as principal the account earns 15%interest compounded quarterly how much will she earn after 5 years
We can solve this by means of the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A is the amount of money saved after a time t, r is the rate of interest in decimal, n is the number of times interest is compounded per year and P is the initial amount deposited in the account.
From the statement of the question we know:
P = $100
r = 0.15
n = 4
t = 5 years
we can replace these values into the above formula, to get:
[tex]A=100(1+\frac{0.15}{4})^{4\times5}=208.81[/tex]Then, after 5 years she will have saved $208.81, subtracting the initial amount of money deposited we get the money earned, like this:
money earned = $208.81 - $100 = $108.81
Then, Mandy earns $108.81 after 5 years.
FDT of weightShow the steps in the construction of the FDT
Okey Im going to explain you how to fill each part of the chart
Tha main part of the FDT is frecuency, for this you are going to take each weight you have, in order
41
42
44
46
etc...
Then you are going to put the frecuency, the frecuency is the number of times each value is in your data list
41 1
42 1
44 4
46 1
etc ....
Now, in this example they are asking you to set some intervals, on range for the class (minimun, maximum). Then some intervals inside this range, so you dont have to put each possible value. Something like this:
41 to 44 6
45 to 48 5
etc...
I need help with this question. Not sure if i have to use sum formula or not
Answer
On the seventh day, 93,312 mails need to be sent.
Explanation
This question has a setup of a geometric progression.
The general form of a geometric progression is
aₙ = a rⁿ⁻¹
where
aₙ = nth term
a = first term = 128
r = common ratio = 3
n = number of days
So, for this question,
aₙ = a rⁿ⁻¹
aₙ = 128 (3ⁿ⁻¹)
On the first day, n = 1
aₙ = 128 (3ⁿ⁻¹)
a₁ = 128 (3¹⁻¹)
a₁ = 128 (3⁰) = 128 (1) = 128
On the seventh day, n = 7
aₙ = 128 (3ⁿ⁻¹)
a₇ = 128 (3⁷⁻¹)
a₇ = 128 (3⁶) = 128 (729) = 93,312
Hope this Helps!!!
I’m supposed to prove this identity but it’s not working for me
Given
[tex](cot\theta+tan\theta)^2=csc^2\theta+sec^2\theta[/tex]Explanation
From the left hand sie
[tex]\begin{gathered} (cot\theta+tan\theta)^2=cot^2\theta+2cot\theta tan\theta+tan^2\theta \\ Next \\ since\text{ tan}^2\theta=sec^2\theta-1\text{ and }cot^2=csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2cot\theta tan\theta+csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2\frac{cos\theta}{sin\theta}\times\frac{sin\theta}{cos\theta}+csc^2\theta-1 \\ (cot\theta+tan\theta)^2=sec^2\theta-1+2+csc\theta-1 \\ (cot\theta+tan\theta)^2=csc^2\theta+sec^2\theta \end{gathered}[/tex]A community recently converted an old railroad corridor into a recreational trail. The graph at the right shows a map of the trail on a coordinate grid. The community plans to construct a path to connect the trail to a parking lot. The new path will be perpendicular to the recreational trail.A. Write an equation of the line representing the new path. B. What are the coordinates of the point at which the path will meet the recreational trail?
The equation of a line is represented by the equation y = mx+c where
m is the slope
c is the intercept
Slope of the line = y2-y1/x2-x1
slope of the line = 150-0/150-75
slope of te line = 150/75
slope of the line = 2
intercept is a point where the line cuts the y axis
The new path cuts the y axis at 100. Hence c = 100
The equation becomes y = 2x=100
2) The coordinates of the point where the path will meet recreational line is arounsd (80, 20) on the graph. THe line will cut the rereational line at this coordinates to make it perpendicular to the line recreation
The perimeter of the rectangle below is 166 units. Find the length of side AB.Write your answer without variables.D4xС5x+2AB =0ХА
The working equation to find the perimeter of the rectangle is:
[tex]P=2L+2W[/tex]where L is the length of the rectangle and W is the width of the rectangle. Given the two sides of the rectangle and its parameter, we can rewrite the equation as:
[tex]166=2(4x)+2(5x+2)[/tex]Simplifying the equation and solve for x, we have:
[tex]\begin{gathered} 8x+10x+4=166 \\ 18x=166-4 \\ \frac{18x}{18}=\frac{162}{18} \\ x=9 \end{gathered}[/tex]For the side of AB that is the same as side AD, the measurement would be:
[tex]AB=5(9)+2=47[/tex]Answer: AB = 47
Find the value of x and y.
By applying the Pythagorean theorem and employing tan values, the values of x and y are 9 and 18, respectively.
The Pythagorean Theorem is what?According to the Pythagorean Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Since base is known to be and tan theta is perpendicular to base,
theta = 30 and x is the perpendicular here.
tan 30 = x/[tex]9\sqrt{3}[/tex]
tan 30 = 1/[tex]\sqrt{3}[/tex]
= x/[tex]9\sqrt{3}[/tex]
x = 9
Using the Pythagorean theorem,
[tex]y^{2} =x^{2} +(9\sqrt{3}) ^{2}[/tex]
the answer is 324: =81+81(3)=81+243
y = [tex]\sqrt{324}[/tex]
y = 18
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find the measure of the missing angle round to the 1 decimal place
To find the missing angle we can use the inentity for cos tha is:
[tex]\cos (\theta)=\frac{adyacent}{hypotenuse}[/tex]and in our triangle will be:
[tex]\cos (\theta)=\frac{24}{30}[/tex]and we cn solve for theta:
[tex]\begin{gathered} \theta=\cos ^{-1}(0.8) \\ \theta=36.9º \end{gathered}[/tex]Write an recursive formula for an, the nth term of the sequence 5, -1, -7,....
The terms of the sequence are 5, -1, -7
Let us find the common difference between each two consecutive terms
-1 - 5 = -6
-7 - (-1) = -7 + 1 = -6
Then the common difference is -6
The first term is 5
The recursive formula is
[tex]a_1=1stterm;a_n=a_{n-1}+d[/tex]Substitute in the formula the value of the 1st term and d the common difference
[tex]a_1=5;a_n=a_{n-1}+(-6)[/tex]Remember (+)(-) = (-)
[tex]a_1=5;a_n=a_{n-1}-6[/tex]This is the recursive formula for the sequence
Solve for x. Round to the nearest tenth, if necessary.N64°хx3.7LM
The triangle is shown below:
Using the Cosine Trigonometric Ratio,
[tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex]We can substitute the values as follows:
[tex]\cos 64=\frac{3.7}{x}[/tex]Solving, we have
[tex]\begin{gathered} 0.4384=\frac{3.7}{x} \\ \therefore \\ x=\frac{3.7}{0.4384} \\ x=8.4 \end{gathered}[/tex]The value of x is 8.4
Identify the probability of choosing a heart card from a deck of cards.1/21/31/41/5
To answer this question, we need to remember that:
1. A typical deck of cards has 52 cards, and they are of the following kinds:
• 13 ---> Spades
,• 13 ---> Hearts
,• 13 ---> Clubs
,• 13 ---> Diamonds
2. Therefore, we have, in total:
[tex]13*4=52\text{ cards}[/tex]3. Since we need the probability of choosing a heart card from a deck of cards, then we have that this probability is:
[tex]\begin{gathered} P(Heart)=\frac{13}{52}=\frac{13}{13*4}=\frac{13}{13}*\frac{1}{4}=\frac{1}{4} \\ \\ P(Heart)=\frac{1}{4} \end{gathered}[/tex]That is, we have 13 cases from the possible 52.
Therefore, in summary, the probability of choosing a heart card from a deck of cards is 1/4 (third option).
Between what two consecutive integers does √68 fall?
The two consecutive integer which the square root of 68 is in between are 8 and 9 , since the square root of 68 is around 8.25
In simple terms, integers means whole and it can't have a fractional or decimal component. So the answer is 8 and 9
(VIEW THE IMAGE) Identify the step where the student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. And how would you correct the mistake? This would be very helpful for me :)
The place where there was a mistake was in the second step of the equation.
What is an equation?It should be noted that an equation is used to show the relationship between the variables by equating them.
From the information, the equation is illustrated as:
-4(x - 15) + 5(-4x - 6y)
Multiply the values outside the parentheses by the values inside it.
= -4x + 60y -20x - 30y
Combine like terms
= -4x - 20x + 60y - 30y
= -24x + 30y
It should be noted that in the second step, In this place, the person didn't multiply the values well.
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graph the equation using the point and the slopey-2=1/5(x-1)
point-slope form of a line:
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1, y1) is a point on the line.
In the case of:
[tex]y-2=\frac{1}{5}(x-1)[/tex]the slope is 1/5 and the point is (1, 2)
With this information, we can deduce that the point (1+5, 2+1) = (6, 3) is on the line. Connecting these two points we can graph the line as follows:
In the circle, what is the measure of ZACB? 60° 20° 80 40°
The given problem is an example of an "inscribed angle"
The inscribed angle ∠ACB is half of the intercepted arc AB
[tex]\angle ACB=\frac{1}{2}\text{mAB}[/tex]The intercepted arc AB is 40°
So, the inscribed angle ∠ACB becomes
[tex]\begin{gathered} \angle ACB=\frac{1}{2}(40\degree) \\ \angle ACB=20\degree \end{gathered}[/tex]Therefore, the measure of ∠ACB is 20°
Dave opens a savings account that has an annual simple interest rate of 0.1%. If he initially deposits $1500, find the amount in the savings account after 5 years.
Answer:
$1,507.51502
Step-by-step explanation:
so we know that %0.1 percent is 0.01. so you are gonna multiply 1500 by 1.001 (just adding the intrest) and then you will get 1501.5. the multiply that by 1.001 again and then then thatanswer and repeat 3 more times and then you get $1.507.51502
Exponential Growth Calculus need help
Answer:
(a) P(t) = 50·17.5^(t/1.5) or P(t) = 50·e^(1.9081t)
(b) P(5) ≈ 695,713
(c) P'(5) ≈ 1,327,514
(d) 4.5 hours
Step-by-step explanation:
You want the exponential function that describes bacterial growth from 50 cells to 875 cells in 1.5 hours, the population after 5 hours, and its rate of growth at that time. You also want to know the time at which the population reaches 250,000.
Exponential growthThe function that models exponential growth can be written as ...
population = (initial population)×(growth factor)^(t/period)
where (growth factor) is the population multiplier over the period.
(a) ExpressionHere, we are given an initial population of 50, and a growth factor of 875/50 = 17.5 in a period of 1.5 hours. This means we can write the function as ...
P(t) = 50(17.5^(t/1.5))
Note that the exact problem statement values are used, so no rounding is required.
If this is expressed using an exponent with a base of 'e', then we have ...
P(t) = 50e^(kt)
Comparing this to the above expression, we see ...
e^(kt) = 17.5^(t/1.5)
k = ln(17.5)/1.5 ≈ 1.9081 . . . . take natural logs and divide by t
So, ...
P(t) ≈ 50(e^(1.9081t))
(b) P(5)
The cell count after 5 hours is modeled as ...
P(5) = 50·e^(1.9081·5)
P(5) ≈ 695,713
(c) P'(5)Differentiating the population function, we have ...
P'(t) = 50·(1.9081)(e^(1.9081t) ≈ 95.4067e^1.9081t
Then the rate of change of the population at t=5 is ...
P'(5) = 1.9081·P(5)
P'(5) ≈ 1,327,514
(d) P^-1(250,000)The time required for the population to reach 250,000 can be found from ...
250,000 = 50·e^(1.9081t)
5,000 = e^(1.9081t) . . . . . . . divide by 50
ln(5,000) = 1.9081t . . . . . . . take natural logs
t = ln(5,000)/1.9081 . . . . . .divide by the coefficient of t
t ≈ 4.5
It will take about 4.5 hours for the population to reach 250,000.
which option below is the correct domain and range of the following function? f(x)= x^1/3 *PHOTO*
The Solution:
Given:
[tex]f(x)=x^{\frac{1}{3}}[/tex]Required:
Find the domain and range of the given function.
Below is the graph of the function:
From the above graph, we have the domain and the range as:
[tex]\begin{gathered} Domain=(-\infty,\infty) \\ \\ Range=(-\infty,\infty) \end{gathered}[/tex]Answer:
[option B]
Teresa purchased a prepaid phone card for $25. Long distance calls cost 19 cents a minute using this card. Teresa used her card only once to make a long distance call. If the remaining credit on her card is $17.02, how many minutes did her call last?Please help me. Its due in a couple of hours.
We have that the prepaid phone card has $25 but Teresa used it and then it has $17.02, then the difference is:
[tex]25-17.02=7.98[/tex]this means that Teresa spent $7.98 on her call, then, if one minute costs 19 cents (or $0.19), then, dividing 7.98 by 0.19 we have:
[tex]\frac{7.98}{0.19}=42[/tex]therefore, Teresa called for 42 minutes.
A new long-life tire has a tread depth of 1/4 inch, instead of the more typical 5/32 inch. How much deeper is the tread on the new tire?The tread on the new tire is ___ inch deeper.(Simplify your answer. Type an integer or a fraction.)
To find how much deeper is the tread on the new tire, we just need to find the difference between the tread depth of this tire to the standard. To find this difference, we subtract the standard from the tread depth of this tire.
[tex]\frac{1}{4}-\frac{5}{32}[/tex]To realize this operation, we need both fractions to have the same denominator. If we multiply both numerator and denominator of a fraction by the same number, the fraction stays the same.
Since 32 is a multiple of 4, we can multiply the first fraction(both numerator and denominator) by 8 to put both fractions with the same denominator.
[tex]\frac{1}{4}\times\frac{8}{8}=\frac{8}{32}[/tex]Now, we can rewrite our operation
[tex]\frac{1}{4}-\frac{5}{32}=\frac{8}{32}-\frac{5}{32}[/tex]When we're doing an addition or subtraction between two fractions with the same denominator, we just need to do the operation on the numerator.
[tex]\frac{8}{32}-\frac{5}{32}=\frac{8-5}{32}=\frac{3}{32}[/tex]The tread on the new tire is 3/32 inch deeper.
Solve the system by graphing. (If there is no solution, enter NO SOLUTION.)y < −2x + 2y≥−x − 2
Okay, here we have this:
Considering the provided system of inequations, we are going to solve the system by graphing, so we obtain the following:
And the solution of a system corresponds to the segments where it intersects, that is to say that in this case it is the dark purple section. The solution to the system will be the area where the shadows of each inequality overlap. Finally we obtain that the system has unlimited solutions.
if income tax expenses had been 23 % what would the net incime have been
EXPLANATION
The next income should be a 23% or 1.23 more the next month.
Each glass of sparkling cranberry juice combines half a cup of cranberry juice and inc cup of sparkling water. Cranberry juice costs $1.50 per cup, and sparkling water costs $.48 per cup. How much will y glasses of sparkling cranberry juice cost in dollars?
The cost of y glasses of sparkling cranberry juice is $2. 24
What are algebraic expressions?Algebraic expressions are described as expressions that consist of variables, factors, constants, terms and coefficients.
They are also described as expressions made up of mathematical operations, which includes;
AdditionSubtractionParenthesesBracketDivisionMultiplication, etcFrom the information given, we have that;
Cranberry juice costs $1.50 per cupSparkling water costs $1.48 per cupA glass is a combination of half cup of cranberry and one cup of sparking waterCost of y glasses of sparkling cranberry juice = 1/2($1.48) + 1($1.50)
Find the product
y = $0.74 + $1.50
Add the values
y = $2. 24
Hence, the value is $2. 24
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-3x-6=9x+6 let's if we on the same page
Answer:
The solution to the equation is;
[tex]x=-1[/tex]Explanation:
Given the equation;
[tex]-3x-6=9x+6[/tex]firstly, let us subtract 6 from both sides;
[tex]\begin{gathered} -3x-6-6=9x+6-6 \\ -3x-12=9x \end{gathered}[/tex]then we can add 3x to both sides;
[tex]\begin{gathered} -3x+3x-12=9x+3x \\ -12=12x \end{gathered}[/tex]lastly, divide both sides by 12;
[tex]\begin{gathered} \frac{-12}{12}=\frac{12x}{12} \\ -1=x \\ x=-1 \end{gathered}[/tex]Therefore, the solution to the equation is;
[tex]x=-1[/tex]
Which of the following rational functions is graphed below?
A. F(x)= -1/x
B. F(x)= 1/x-1
C. F(x)= 1/x+1
D. F(x)= 1+x/x
Because we have a vertical asymptote at x = -1, we conclude that the correct option is C.. Which of the following rational functions is graphed below? In the graph, we can see that we have a vertical asymptote at x = -1.. …
Measure the width of a standard sized piece of paper (printer paper works great) in millimeters. Choose the answer that best represents the correct number of significant figures allowed by the ruler and is closest to your measured value.Group of answer choices216 mm215.9 mm21.59 mm
the width of a standard sized piece of paper in millimeters is 215.9mm
therfore from the grooup of answer choices, the second option which is 215.9mm is the correct answer
Janet cleans 25 of her bedroom that she shareswith her sister Mary. Mary also cleans 2/3 of theirshared bedroom. How much of the bedroom hasbeen cleaned by Janet and Mary?
Given
Janet = 25%
Mary = 2/3 = 66.66%
Procedure
Total = 25% + 66.66% = 91.66%
In fraction
11/12
