ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]$800 is deposited in a bank account which is compounded continuously at 8.5% annual interest rate. The future balance of the accourby the function: A = 800e0.085t. How long will it take for the initial deposit to double? Round off to the nearest tenth of a year.
Given:
Function :
[tex]A=800e^{0.085t}[/tex]Initial deposit =$800
Annual interest rate =8.5%
[tex]A=A_0e^{rt}[/tex]Where,
[tex]\begin{gathered} A=\text{Amount after t time} \\ A_0=\text{Initial amount} \\ r=\text{interest rate} \\ t=\text{time} \end{gathered}[/tex][tex]\begin{gathered} r=\frac{8.5}{100} \\ r=0.085 \end{gathered}[/tex]When deposit is double of initial deposit .
[tex]\begin{gathered} 2\times800=800e^{0.085t} \\ \frac{2\times800}{800}=e^{0.085t} \\ 2=e^{0.085t} \\ \ln 2=\ln e^{0.085t} \\ 0.085t=0.69314 \\ t=\frac{0.69314}{0.085} \\ t=8.15 \end{gathered}[/tex]So after 8.15 year initial amount will be double.
I narrowly answered the first question on my homework but for some reason EF really confuses me.
Solution
Part 1
For this case we can find DF with the following proportion formula:
[tex]\frac{AC}{AB}=\frac{DF}{DE}[/tex]And replacing we got:
[tex]\frac{4}{2}=\frac{DF}{1.34},DF=2.68[/tex]Part 2
[tex]\frac{BC}{AB}=\frac{EF}{DE}[/tex]And solving for EF we got:
[tex]EF=1.34\cdot\frac{3}{2}=2.01[/tex]7/9 + 2/7pls help me
We have to sum fractions:
[tex]\frac{7}{9}+\frac{2}{7}=\frac{7\cdot7+2\cdot9}{7\cdot9}=\frac{49+18}{63}=\frac{67}{63}[/tex]Higher Order Thinking Leah wrote 2 different fractions with the same denominator. Both fractions were less than 1. Can their sum equal 1? Can their sum be greater than 1? Explain.
1) Gathering the data
2) Since we don't know exactly their numerators we can write, for instance, two fractions with the same bottom number and lesser than 1:
[tex]\begin{gathered} \frac{1}{4},\text{ }\frac{3}{4} \\ \frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1 \\ \frac{2}{4}+\frac{3}{4}=\frac{5}{4}=1.25 \\ \frac{1}{5}+\frac{3}{5}=\frac{4}{5}=0.8 \end{gathered}[/tex]2) Hence, we can conclude that the sum can be equal to 1, greater than 1, and lesser than 1. That'll depend on the numerator, and the fractions Leah can pick.
3) So, they can be less, equal to, and greater than 1.
Jada has 4 meters of ribbon. How many pieces of ribbon of length 1/3 meter can she cut from it. Draw a diagram to illustrate your solutions.
She can cut twelve 1/3 meters from 4 meters.
The diagram is shown in the explanation below.
Explanation:Parameters:
Total length of ribbon = 4 meters
Let x represent the number of 1/3 meters she can cut, then
[tex]\begin{gathered} \frac{1}{3}x=4 \\ x=4\times3=12 \end{gathered}[/tex]She can cut twelve 1/3 meters from 4 meters.
This is illustrated in the diagram below:
a dime, a nickel, and a penny are each tossed one time. which table shows all the possible ways the coins could land face up, using H for heads and T for tails?
GIVEN:
We are told that an experiment consists of tossing a dime, a nickel and a penny, each of them once.
Required;
Select which table shows all the possible ways the coins could land face up, using H for heads and T for tails.
Step-by-step solution;
First we consider the entire sample space for the experiment, and that is all the possible outcomes for this experiment. This is shown below;
[tex]HHH,\text{ }HHT,\text{ }HTH,\text{ }THH,\text{ }TTH,\text{ }THT,\text{ }HTT,\text{ }TTT[/tex]The second table shows the possible outcomes whereby all coins lands face up without any outcome of landing tails up, that is TTT. Tables 1, 3 and 4 shows possibilities of having a tails for every throw in one of the outcomes (that is, TTT).
Therefore table 2 is the only set of outcomes where the coins could land face up.
ANSWER:
Table 2 (second option).
Frank has a circle Garden the area of the garden is 100 ft² what is the approximate distance from the edge of Frank's garden to the center of the garden ? (A = pi r²)
The area of a cirle is given by
[tex]A=\pi(R^2)\text{ where R is the radius, the distance from the edge/circumference to the centre}[/tex]We seek to find R, so let us make it the subject of the formula;
[tex]R=\sqrt[]{\frac{A}{\pi}}[/tex][tex]\begin{gathered} R=\sqrt[]{\frac{100}{3.142}} \\ R=5.64\approx6ft \end{gathered}[/tex]Therefore, the approximate distance from the edge of Frank's garden to the center of the garden is 6ft
5 markers cost $6.55.Which equation would help determine the cost of 4 markers?
5 markers -------> $6.55
4 markers -------> x
[tex]undefined[/tex]What is the value of the expression belowwhen y = 9 and z = 3?10y - 7z
y= 9 & z = 3
10y - 7z
put y= 9 & z = 3
= 10 (9) - 7(3)
= 90 - 21
= 69
so the answer is 69
can you help me with this? i am looking for perimeter and and area
For this problem, we are given a rectangle with the measurement of its dyagonal and the angle between the dyagonal and the base. We need to determine the perimeter and area for this rectangle.
For this, we need to analyze the right triangle that is formed between the dyagonal, the width and height of the rectangle. This triangle is shown below:
From the image above, we can notice that the height is the opposite side to the known angle. Therefore we can calculate it by using the sine relation on a right triangle.
[tex]\begin{gathered} \sin 29=\frac{\text{ height}}{18} \\ \text{height}=18\cdot\sin 29 \\ \text{height}=18\cdot0.48 \\ \text{height}=8.73 \end{gathered}[/tex]The rectangle's height is equal to 8.73 ft.
On the other hand the width is the adjascent side to the known angle, therefore we can calculate it by using the cossine relation.
[tex]\begin{gathered} \cos 29=\frac{\text{ width}}{18} \\ \text{width}=18\cdot\cos 29 \\ \text{width}=18\cdot0.87 \\ \text{width}=15.74 \end{gathered}[/tex]The rectangle's width is equal to 15.74 ft.
Now we can calculate the perimeter and area for the rectangle.
[tex]\begin{gathered} P=2\cdot(\text{width}+\text{height)} \\ P=2\cdot(15.74+8.73) \\ P=2\cdot24.47 \\ P=48.94\text{ ft} \end{gathered}[/tex]The perimeter for the rectangle is 48.94 ft.
[tex]\begin{gathered} A=\text{width}\cdot\text{height} \\ A=15.74\cdot8.73 \\ A=137.41 \end{gathered}[/tex]The area for the rectangle is 137.41 square ft.
showing all your work for problem 1 divide simplify and state the domain and problem 2 multiply simplify and state the domain
The domain of the problem is given as
[tex](-\infty,\text{ 0) U (0, +}\infty)[/tex]Evaluate 0^0.
Provide justifications for your conclusion.
The power expression 0⁰ leads to an indetermination.
What is the result of 0⁰ according to algebra properties?Let be the power expression 0⁰, whose result has to be found by means of algebra properties, especially those related to operations between powers. First, write the entire expression:
0⁰
Second, use the existence property of additive inverse:
0ⁿ ⁺ ⁽⁻ⁿ⁾, where n is a real number.
Third, use power properties:
0ⁿ · 0⁻ⁿ
0ⁿ · (0ⁿ)⁻¹
0 · 0⁻¹
Fourth, by definition of division:
0 / 0
The term 0 / 0 represents an indetermination.
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choose the x-intercept and the y-intercept for each equationx+4y=24a (0,4)b (0,6)c (6,0)d (24,0)e (24,6)
Given:
The equation is x + 4y = 24
Required:
Find the x - intercept and y - intercept?
Explanation:
We know that
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]Where, a is x - intercept
and b is y - intercept
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
Now,
[tex]\begin{gathered} x+4y=24 \\ \frac{x}{24}+\frac{y}{6}=1 \end{gathered}[/tex]From this we can say that x - intercept (24, 0) and y - intercept (0, 6).
Answer:
Hence, (24, 0) and (0, 6) are intercept of given equation.
2Select all values of x that make the inequality -x + 8 >11 true.A-2B-6С-4D1E3F.-3
To solve this problem, we need to know which values of x would make the inequality -x + 8 > 11 true.
To do this, we will need to solve the equation in terms of x, just like how we normally solve for x in any linear equation.
[tex]-x+8>11[/tex]Using the Addition Property of E
Write the function graphed below in the form g(x)… reference photo
We will have the following:
First, we can see that the function in the image will have a mother function:
[tex]y=\sqrt[3]{x}[/tex]Where the function has been moved 2 units left, and 2 units down:
[tex]y=\sqrt[3]{x+2}-2[/tex]Now, we known that the function has been expanded on the vertical, so:
[tex]y=a\sqrt[3]{x+2}-2[/tex]Now, we solve for "a" while we replace for a value of the function, we can see that (6, 4) belongs, so:
[tex]\begin{gathered} 4=a\sqrt[3]{6+2}-2\Rightarrow4=a\sqrt[3]{8}-2 \\ \\ \Rightarrow6=2a\Rightarrow a=3 \end{gathered}[/tex]So, the equation of the function will be:
[tex]g(x)=3\sqrt[3]{x+2}-2[/tex]This can be seeing as follows:
A rock is thrown upward from the top of a 80-foot high cliff overlooking the ocean at a speed of 64 feetper second The rock's height above ocean can be modeled by the equationH (t) = -16t^2 +64t + 80.a. When does the rock reach the maximum height?The rock reaches its maximum height after ________second(s).b. What is the maximum height of the rock?The maximum height obtained by the rock is_______feet above sea level.c. When does the rock hit the ocean?The rock hits the ocean after_____seconds.
Given:
The speed is 64 feet per second.
The height of the high cliff is 80 feet.
The function is
[tex]H(t)=-16t^2+64t+80[/tex]a)
We need to find the maximum value of t in the given function to find a time when the rock reaches its maximum height.
Differentiate the given equation, we get
[tex]H^{\prime}(t)=-16(2t)^{}+64[/tex][tex]H^{\prime}(t)=-32t^{}+64[/tex]Set H'(t)=0 and solve for t.
[tex]0=-32t^{}+64[/tex]Adding 32t on both sides, we get
[tex]0+32t^{}=-32t+64+32t[/tex][tex]32t^{}=64[/tex]Dividing both sides by 32, we get
[tex]\frac{32t}{32}^{}=\frac{64}{32}[/tex][tex]t=2[/tex]Hence the rock reaches its maximum height after 2 seconds.
b)
Substitute t=2 in the given equation to find the maximum height of the rock.
[tex]H(2)=-16(2)^2+64(2)+80[/tex][tex]H(2)=144[/tex]Hence the maximum height obtained by the rock is 144 feet above sea level.
c)
Substitute H(t)=0 in the given function to find the time when the rock hit the ocean.
[tex]0=-16t^2+64t+80[/tex]Dividing both sides by (-16), we get
[tex]0=-\frac{16t^2}{-16}+\frac{64t}{-16}+\frac{80}{-16}[/tex][tex]0=t^2-4t-5[/tex][tex]t^2-4t-5=0[/tex][tex]t^2+t-5t-5=0[/tex][tex]t(t+1)-5(t+1)=0[/tex][tex](t+1)(t-5)=0[/tex][tex](t+1)=0,(t-5)=0[/tex][tex]t=-1,t=5[/tex]Omitting the negative value, we get t= 5 seconds.
Hence the rock hits the ocean after 5 seconds.
Six times a number is greater than 20 more than that number. What are the possible values of that number?a. n<4b. n>4c. n>20/7d. n<20/7
Let's call n to the number of interest. The following inequality represents this problem:
6n > 20 + n
Solving for n
6n - n > 20
5n > 20
n > 20/5
n > 4
Solve Brain Teaser
Write an expression that has a value of 40 using two operations and each of the numbers 1, 2, 3, 4, and 5 exactly once.
More Rules for Your Expression
You can use parentheses or other grouping symbols.
You can make one of your numbers an exponent.
You can use either operation as many times as you like, but you can use each number only one time in the expression.
Bonus Challenge
This brain teaser has more than one solution. Can you find one more?
The required expression is given as 2×4×5, this gives the value 40.
Given that,
To write an expression that has a value of 40 using two operations and each of the numbers 1, 2, 3, 4, and 5 exactly once.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
From the multiple iterations, we have to choose appropriate numbers,
first the greatest multiplied value can be calculated by two number is given as,
4 × 5 = 20,
Now we have to determine only one operation.
So when we multiply 20 by 2 we get 40,
So.
40 = 2×4×5
Thus, the required expression is given as 2×4×5, this gives the value 40.
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not college I misclicked but the question is in pic
Answer
x = 13.33 units
Explanation
We can easily tell that the small triangle (with sides 6 and 8) is similar to the bigger triangle with sides (6+4 and x).
And the ratio of corresponding sides is the same for two similar triangles.
From the image, we can see that
6 is corresponding to (6 + 4)
8 is corresponding to x
So,
[tex]\begin{gathered} \frac{6}{6+4}=\frac{8}{x} \\ \frac{6}{10}=\frac{8}{x} \end{gathered}[/tex]We can now cross multiply
6x = (8) (10)
6x = 80
Divide both sides by 6
(6x/6) = (80/6)
x = 13.33 units
Hope this Helps!!!
QuestioA team of physicians is studying a weight-loss pill. They recruited volunteers for a study. The volunteers were in the agegroup of 30 to 35 and were more than 40 pounds overweight. The physicians gave the new weight-loss pill pack to onegroup. The other group received a pill pack that resembled the new weight-loss pill pack but was a placebo. In thedescription of the above situation, determine the experimental group
The experimental group will be the group who received the new weight-loss pill. This group will be used to identify or estimate the effect of the variable or the ingredient which will cause weight loss.
The other group who received the resemblanced of the new weight-loss pill but placebo will only be used for the comparison effect from the experimental group.
So the answer will be :
1st Option, The group that received the new weight-loss pill pack is the experimental group.
A roll of 50 dimes weighs 4 ounces. Which proportion can be used to find the weight in ounces, w, of 300 dimes?
50 dimes = 4 ounces
300 dimes = w ounces
[tex]\begin{gathered} \frac{50}{300}=\frac{4}{w} \\ \frac{1}{6}=\frac{4}{w} \\ w=24 \end{gathered}[/tex]300 dimes = 24 ounces
the proportion is 1/6 =4/w
Let f(x) = x² + 11x + 25 Find a so that f(a) = 1
A=-3
A=-8
Explanation
Step 1
[tex]f(x)=x^2+11x+25[/tex]there is a number A so f(A) =1, then
[tex]\begin{gathered} f(A)=A^2+11A+25 \\ f(A)=1 \\ \text{then} \\ A^2+11A+25=1 \\ A^2+11A+24=0\text{ equation(1)} \end{gathered}[/tex]Step 2
solve using the quadratic equation
[tex]\begin{gathered} \text{for } \\ ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]a)let
a=1
b=11
c=24
the variable is A,
b) replace
[tex]\begin{gathered} A=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ A=\frac{-11\pm\sqrt[]{121^{}-4\cdot1\cdot24}}{2\cdot1} \\ A=\frac{-11\pm\sqrt[]{121^{}-96}}{2} \\ A=\frac{-11\pm\sqrt[]{25}}{2} \\ A_1=\frac{-11+\sqrt[]{25}}{2}=\frac{-11+5}{2}=\frac{-6}{2}=-3 \\ A_1=-3 \\ A_2=\frac{-11-\sqrt[]{25}}{2}=\frac{-11-5}{2}=\frac{-16}{2}=-8 \\ A_2=-8 \end{gathered}[/tex]I hope this helps you
Jack needs to order some new supplies for the restaurant where he works. The restaurant needs at least 711 glasses. There are currently 206 glasses. If each set on sale contains 10 glasses, write and solve an inequality which can be used to determine ss, the number of sets of glasses Jack could buy for the restaurant to have enough glasses.
Jack needs to buy at least 51 sets of glasses to ensure that the restaurant has enough glasses.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Let s be the number of sets of glasses that Jack needs to buy.
According to the problem, the restaurant needs at least 711 glasses, and currently has 206. So Jack needs to buy:
711 - 206 = 505 glasses
Since each set contains 10 glasses, the total number of glasses Jack can buy is:
10s
To have enough glasses, the total number of glasses Jack buys must be greater than or equal to 505. So we can write the inequality:
10s ≥ 505
To solve for s, we can divide both sides by 10:
s ≥ 50.5
Since s must be a whole number (you can't buy half a set of glasses), we round up to the nearest integer:
s ≥ 51
Therefore, s ≥ 51.
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Pre-Calculus_Unit 1_Math_20-21 / 4 of 16 Find the slope of the line determined by the equation 3x +10y = 11 O A. m = -3 OB. m= 3 O C. 3 m=- 10 11 10 Em: -10
Brook, this is the solution:
Let's find the slope for this equation:
3x + 10y = 11
10y = -3x + 11
Dividing by 10 at both sides:
10y/10 = -3x/10 + 11/10
y = -3x/10 + 11/10
Therefore,
m = -3/10
If you make $13.00/hour at your job and you work on average 35 hours a week, how much do you bring home if you get $80 taken out in taxes????
If you make $13/ hour and you work 35 hours, you make:
[tex]13\cdot35\text{ = \$455}[/tex]Then, you substract the $80 in taxes:
[tex]455-80\text{ = \$375}[/tex]So in total, you should bring home $375
What is the answer for this question? Why would it be helpful to rewrite the equation that way?
To solve the equation for "x", we will use operations in both sides of the equation.
[tex]3x+5y=500[/tex]First, we already have the "x" in the left side, but there is also a term with "y", so let's put it to the right side.
to do this, we can substract "5y" in both sides:
[tex]\begin{gathered} 3x+5y-5y=500-5y \\ 3x=500-5y \end{gathered}[/tex]Now, we just need to pass the "3" to the other side, which we can do by dividing both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{500-5y}{3} \\ x=\frac{500}{3}-\frac{5}{3}y \end{gathered}[/tex]Tha is the equation solved for "x".
This way of writing the equation can be usefull if we want to calculate "x" for a given "y" value, that is, if we know the number of adult tickets sold, we can substitute it into the equation in this form and just evaluate the right part to obtain the "x" value.
what is the perimeter? and what unit should i use?
The given information is:
- 7-gon: it has 7 sides.
- a=15 ft
- s=14 ft
The perimeter, is the sum of the side lengths, as it has 7 sides, then its perimeter is:
[tex]\begin{gathered} P=7s \\ P=7*14ft \\ P=98ft \end{gathered}[/tex]Now, the area is given by the formula:
[tex]\begin{gathered} A=\frac{7}{2}(s*a) \\ \\ A=\frac{7}{2}(14ft*15ft) \\ \\ A=\frac{7}{2}(210ft^2) \\ \\ A=\frac{1470ft^2}{2} \\ \\ A=735ft^2 \end{gathered}[/tex]The area is 735 square feet
You're feeling hungry so you order a 40-piece Chicken Nuggets from McDonalds. It costs $8.99. You have a 10% off coupon, but you also have to pay 10% sales tax. What is the final price? Round your answer to the nearest cent.
In order to calculate the discount of 10%, we can just multiply the number by 90%, that is, 0.9.
And in order to calculate the increase of 10% by the taxes, we can multiply the number by 110%, that is, 1.1.
So, applying both these percentages together, we have:
[tex]\begin{gathered} \text{Price}=8.99\cdot0.9\cdot1.1 \\ \text{Price}=8.9 \end{gathered}[/tex]So the final price will be $8.90.
A polynomial P is given. P(x) = x3 + 3x2 + 6x(a) Find all zeros of P, real and complex.x = (b) Factor P completely.P(x) =
P(x) is defined by the expression
[tex]P(x)=x^3+3x^2+6x[/tex]Note
[tex]x^3+3x^2+6x=x(x^2+3x+6)\text{ }[/tex]Therefore, one solution is 0.
The other two solutions come from
[tex]x^2+3x+6=0[/tex]Apply the general solution in order to find complex solutions
[tex]\frac{-3\pm\sqrt{3^2-4(1)(6)}}{2(1)}=\frac{-3\pm\sqrt{-15}}{2}[/tex]The solutions are
[tex]0,\frac{-3+i\sqrt{15}\text{ }}{2},\frac{-3-i\sqrt{15}}{2}[/tex]We calculate the factor from the solutions, like this
[tex]x=\frac{-3+i\sqrt{15}}{2}\Rightarrow x+\frac{3}{2}-\frac{i\sqrt{15}}{2}=0[/tex][tex]x=\frac{-3-i\sqrt{15}}{2}\Rightarrow x+\frac{3}{2}+\frac{i\sqrt{15}}{2}=0[/tex]The factor is
[tex]P(x)=x(x+\frac{3}{2}-\frac{i\sqrt{15}}{2})(x+\frac{3}{2}+\frac{i\sqrt{15}}{2})[/tex]√10=Rational or Irrational
Square roots are rational only when has perfect square factors.
√10 = √(2*5) = √2 * √5
2 and 5 are not perfect squares, then √2 and √5 are irrational. In consequence, √10 is also irrational.