We will write it as follows:
[tex]3.92\cdot10^7=39200000[/tex]THE TOP OF A 20 FT. WATERSLIDEIS 16 FT. ABOVE THE GROUND.HOW FAR FROM THE BASE OF THESTEPS WILL THE GUESTS BE SHOTINTO THE WATER?
Using the given information, we form the following diagram.
To find x we use Pythagorean's Theorem.
[tex]20^2=16^2+x^2[/tex]Then, we solve for x.
[tex]\begin{gathered} 400-256=x^2 \\ x=\sqrt[]{144} \\ x=12 \end{gathered}[/tex]Therefore, the answer is 12 feet.Which of the following shows that f(x) grows at the same rate as g(x)? (5 points)the limit as x goes to infinity of the quotient of f of x and g of x equals 1000the limit as x goes to infinity of the quotient of f of x and g of x equals 0the limit as x goes to infinity of the quotient of f of x and g of x equals infinityNone of these
The function f(x) grows at the same rate as the function g(x) according to the condition : [tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} =1000[/tex].
We are given two functions. The functions are f(x) and g(x). The definitions of the functions are not given explicitly, but we need to find the relationship between the functions. Both functions grow at a certain rate. We need to find the condition that shows that the function f(x) grows at the same rate as the function g(x). The ratio of the limiting values of the two functions must be a finite and non-zero constant for the functions to have the same rate of growth.
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Sketch a system of two linear equations whose solution is (-1, 3).T
The two system of equations
y = 2x + 3
and
y = -3x has a solution ( -1, 3 )
#(13) Admission to the fair costs $7.75. Each ride costs you $0.50. You have $15 to spend at the fair including admission. Wrtie an inequality to best model this situation. Using the inequality that you chose in #13 what is the maximum number of rides you can go on?
We have the next information
7.75 admission
0.50 ride
you have 15 that is the limit
The inequality will be
[tex]7.75+0.50x\le\text{ 15}[/tex]where x is the number of rides you can do
Using the inequality we can calculate the number of rides, we need to clear x
[tex]\begin{gathered} 0.50x\le15-7.75 \\ 0.50x\le7.25 \\ x\le\frac{7.25}{0.50} \\ x\le14.5 \end{gathered}[/tex]the maximum number of rides is 14 because we can't do a half ride
A line is drawn on a coordinate plane so that it is parallel to the x-axis and passes through the point (4.6). Which statement identifies equation and slope of this line?
A. The equation of the line is y = 6, and the slope is 0
Explanations:Note that:
When a line is parallel to the x -axis, the slope of that line equals to zero
According to the question, the line passes through the point with coordinates (4, 6)
The equation of a line passing through a point of coordinates (x₁ , y₁) is given by the equation:
y - y₁ = m ( x - x₁)
x₁ = 4, y₁ = 6
Substitute x₁ = 4, and y₁ = 6 into the given equation:
y - 6 = 0(x - 4)
y - 6 = 0
y = 6
The equation of the line is y = 6, and the slope is 0
If f(x) = 2x^2 - 5 and g(x) = 2x + 1, evaluate f(g(x)) when x = -3
when x = -3
[tex]\begin{gathered} \Rightarrow[2(2\times-3+1)^2]-5 \\ 2[-5]^2-5=45 \end{gathered}[/tex]The final answer is 45
7+8=15 how do you decompose 10?I'm doing this for my granddaughter she's in the first grade and the teacher wants to know her dude examples 7 + 8 equals 15 and they want her to decompose it to make 10 then and use the number bond to show how you took two
To decompose 10 on basis of 8 it becomes 10 -2 =8
so 8 + 2 =10
A bottlenose dolphin is 10 feet belo sea level. Then it begins to dive at a rate of 9 feet per second. What is the equation of the line that represents its elevation,y, after x seconds
State if the two triangles are congruent and by what thermoe
Although the triangles seems right triangles, we can't assume it because they might be out of scale.
So, the informations we have are:
They have a side wity equal length followed by a common side, thus it also has common length, and followed by an angle with common measure.
This is a case of Side-Side-Angle, and this is not enough to prove congruency.
So, the answer is that, we can't confirm if they are congruent or not.
what is 2/3 times 3/8
Mutiply both fractions:
[tex]\frac{2}{3}\times\frac{3}{8}[/tex][tex]\frac{2\times3}{3\times8}=\frac{6}{24}[/tex]Simplify by 6.
[tex]\frac{1}{4}[/tex]Answer:
Do the multiplication straight across 2 times 3= 6. 3times 8= 24 so 6/24 or 1/4
Manuel has a bag of marbles with 2 blue marbles, 1 white marbles, and 1 red marbles.Find the following probabilities of Manuel drawing the given marbles from the bag if the first marble(s) is(are) returned to the bag after they are drawn.a) a blue, then a red b) a red, then white c) a blue, then a blue, then a blue
Explanation
We are given the following:
[tex]\begin{gathered} Bag=\begin{cases}{2\text{ }blue\text{ }marbles} \\ {1\text{ }white\text{ }marbles} \\ {1\text{ }red\text{ }marbles}\end{cases} \\ Total\text{ }marbles=2+1+1=4 \end{gathered}[/tex]We are required to determine the following probabilities:
[tex]\begin{gathered} (a)\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }red \\ (b)\text{ }a\text{ }red,\text{ }then\text{ }white \\ (c)\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }blue \end{gathered}[/tex]We know that probability is calculated as:
[tex]Prob.=\frac{Number\text{ }of\text{ }required\text{ }outcome}{Number\text{ }of\text{ }possible\text{ }or\text{ }total\text{ }outcome}=\frac{n(E)}{n(S)}[/tex]For Question A:
We can determine the probability of a blue, then a red as:
[tex]\begin{gathered} P(blue\text{ }and\text{ }red)=P(Blue)\times P(Red) \\ =\frac{2}{4}\times\frac{1}{4}=\frac{2}{16}=\frac{1}{8} \\ \therefore P(blue\text{ }and\text{ }red)=\frac{1}{8} \end{gathered}[/tex]For Question B:
We can determine the probability of a red, then white as:
[tex]\begin{gathered} P(red\text{ a}nd\text{ w}h\imaginaryI te)=P(Red)\times P(Wh\imaginaryI te) \\ =\frac{1}{4}\times{}\frac{1}{4}=\frac{1}{16} \\ \operatorname{\therefore}P(red\text{ a}nd\text{ w}h\imaginaryI te)=\frac{1}{16} \end{gathered}[/tex]For Question C:
We can determine the probability of a blue, then blue, then blue as:
[tex]\begin{gathered} P(blue,blue,blue)=P(blue)\times P(blue)\times P(blue) \\ =\frac{2}{4}\times\frac{2}{4}\times\frac{2}{4}=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8} \\ \therefore P(blue,blue,blue)=\frac{1}{8} \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} (a)\text{ }P(blue\text{ }and\text{ }red)=\frac{1}{8} \\ \\ (b)\text{ }P(red\text{ a}nd\text{ w}h\mathrm{i}te)=\frac{1}{16} \\ \\ (c)\text{ }P(blue,blue,blue)=\frac{1}{8} \end{gathered}[/tex]Wesley Snipes ears a monthly salary of $1,685, plus a 8.5% commission on all sales over $2,000 each month. This month, his sales were $6,250. What was his totalincome for the month?$2,224.50$2,175.80$2,112.90$2,046.25None of these choices are correct.
His total income for the month is $2,216.25 and that means none of these choices are correct
Here, we want to get the total income for the month
Now, what we have to add to the monthly salary is the commission percentage amount
From the question, this is simply 8.5% of $6,250
Thus, we have it that;
[tex]\frac{8.5}{100}\times\text{ 6,250 = \$531.25}[/tex]We now proceed to add this to the salary
We have the total as;
[tex]1,685\text{ + 531.25 = \$2,216.25}[/tex]Select ALL the true statements1 poClare created Figure A Then she created Figure B by translating Triangle C and thentranslating Triangle D.Figure AFigureсDFigure A is congruent to Figure BFigure B is a translation of Figure A.Triangle Cis congruent to Triangle CTriangle D'is congruent to Triangle D.
The first statement cannot be true since the complete figure is not the same and sides cannot be overlapped together and look the same without a translation.
The second statement is not true either because if the full figure was translated it would look the same in another position and this is not the case.
The third and forth statements are true because figures were translated and didn't suffer any expansions or contractions which means that all of its sides must be equal and make them congruent.
ate Fatuma Michele Simplify the expression below and identify the property used when eliminating the parentheses. 49 + 18 + 4 (29 + 9.5) 9+ The property was used to eliminate the parentheses. distributive commutative
Simplify the expression
[tex]\begin{gathered} 4q+18+4(2q+9.5)=4q+18+4\cdot2q+4\cdot9.5 \\ =4q+18+8q+38 \\ =12q+56 \end{gathered}[/tex]The distributive property is used to simplify the expression 4(2q + 9.5).
Answers:
12q + 56
Distributive property.
can you show me step by step how to divide 6 1/8 divided by 1 3/4
From the question we are asked to divide 6 1/8 by 1 3/4
To do this, we first convert this improper fraction to proper fraction
6 1/8 = 49/8
1 3/4 = 7/4
The next step is to convert to decimal.
49/8 = 6.125
7/4 = 1.75
So lets divide 6.125 by 1.75
6.125/1.75 = 3.5
Now let's convert the decimal back to fraction
3.5 in fraction = 7/2 = 3 1/2
So, 6 1/8 divide by 1 3/4 = 3 1/2
You have a line AB where A is (0,3) and B is (2,7) find a point P that partitions the line 1:2.
ANSWER:
[tex]P=(\frac{2}{3},\frac{13}{3})[/tex]STEP-BY-STEP EXPLANATION:
We have the following formula to calculate the point P
[tex]\begin{gathered} x_p=\frac{x_2\cdot a+x_1\cdot b}{a+b}_{} \\ y_p=\frac{y_2\cdot a+y_1\cdot b}{a+b}_{} \\ a\colon b=1\colon2 \\ (x_1,y_1)=(0,3) \\ (x_2,y_2)=(2,7) \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} x_p=\frac{2\cdot1+0\cdot2}{1+2}=\frac{2+0}{3}=\frac{2}{3} \\ y_p=\frac{7\cdot1+3\cdot2}{1+2}=\frac{7+6}{3}=\frac{13}{3} \\ \text{The point p is:} \\ (\frac{2}{3},\frac{13}{3}) \end{gathered}[/tex]What is the slope of the line in the graph?A. 8B. 1/8C. 1/4 D. 4
The slope of a line graph can be found using the formula:
[tex]\begin{gathered} slope\text{ = }\frac{y_2-\text{ y}_1}{x_2-x_1} \\ Where\text{ \lparen x}_1,y_1)\text{ and \lparen x}_2,y_2)\text{ are two points on the line} \end{gathered}[/tex]From the graph, we have the points (0,0) and (8, 2)
Substituting the values into the formula:
[tex]\begin{gathered} slope\text{ = }\frac{2-0}{8-0} \\ =\text{ }\frac{2}{8} \\ =\text{ }\frac{1}{4} \end{gathered}[/tex]Answer:
slope = 1/4 (Option C)
1. Problem Set B: For each of the following problems, include a sketch of the scenario, name the characteristic the question is asking for and how you will solve for that characteristic. An object is dropped from a bridge over a bay. Its motion is modeled by the quadratic equation h(t) = -16t^2 +56 where t represents the time since the object was dropped and h(t) represents the height of the object. a. How long will it take for the object to reach the water?b. How will you find this characteristic?c. What is the meaning of the 56 in the equation h(t) = -16t^2 + 56? a. It takes 56 seconds for the object to reach the ground. b. The object is 56 feet above the ground initially. c. The object reaches its maximum height after 56 seconds.
we have the equation
h(t) = -16t^2 +56
Part a. How long will it take for the object to reach the water?
when the object reach teh water h(t)=0
so
For h(t)=0
solve for t
0=-16t^2+56
16t^2=56
t^2=56/16
t^2=3.5
t=(+/-)1.87
therefore
answer part a is t=1.87 secRemember that the time can not be negative
Part b. How will you find this characteristic?
because if the object reach the water is when the height is zero (sea level is the zero)Part c. What is the meaning of the 56 in the equation h(t) = -16t^2 + 56?
answer is
b. The object is 56 feet above the ground initially.I have a calculus question about the definite integral, from my high school AP Calculus Class, pic included
Given the following definite integral.
[tex]\int_{-4}^4\sqrt{4^2-x^2}dx[/tex]We will use the substitution to solve the definite integral
Let the following:
[tex]\begin{gathered} 4sin(\theta)=x \\ 4cos(\theta)*d\theta=dx \\ And: \\ 4^2-x^2=4^2-4^2sin^2\theta=4^2(1-sin^2\theta)=4^2cos^2\theta \end{gathered}[/tex]Substitute into the given integral:
[tex]\begin{gathered} \int_{-4}^4\sqrt{4^2-x^2}dx=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sqrt{4^2cos^2\theta}*4cos(\theta)*d\theta \\ \\ =\int_{-\pi/2}^{\pi/2}4cos\theta *4cos\theta *d\theta=\int_{-\pi/2}^{\pi/2}16cos^2\theta *d\theta \end{gathered}[/tex]Now, we will use the following identity:
[tex]cos^2\theta=\frac{1}{2}(1+cos2\theta)[/tex]So, the integral will be:
[tex]\begin{gathered} =\int_{-\pi/2}^{\pi/2}\frac{16}{2}(1+cos2\theta)d\theta \\ \\ =8(\theta+\frac{1}{2}sin2\theta) \end{gathered}[/tex]substitute θ = π/2, and θ = -π/2
So, the value of the integral =
[tex]8*(\frac{\pi}{2}-(-\frac{\pi}{2}))=8π[/tex]So, the answer will be: Area = 8π
The graph of the given function is shown in the following picture
Express your answer as a polynomial in standard form.9f(x) = x2 - 4x –g(x) = -3x – 5Find: f(g(x))
Given the functions:
[tex]\begin{gathered} f(x)=x^2-4x-9 \\ g(x)=-3x-5 \end{gathered}[/tex]We need to find the function f(g(x)
So, every variable for x in the function f(x) will be substituted with g(x) as follows:
[tex]f(g(x))=(-3x-5)^2-4\cdot(-3x-5)-9[/tex]Now, we will simplify the expression:
[tex]\begin{gathered} f(g(x))=9x^2+30x+25+12x+20+9 \\ \\ f(g(x))=9x^2+42x+54 \end{gathered}[/tex]So, the answer will be:
[tex]f(g(x))=9x^2+42x+54[/tex]As part of a class project, a university student surveyed students in the cafeteria to look for a relationship between the students' eye color and hair color. The table contains the survey results. Match the descriptions with the correct values.
Ok, so
If we analyze the tab, we notice the following things:
- The number of students with blue eyes and blond hair is 42. That's because if we go to the table and look at the rows and columns, 42 is the number which relations these two facts.
- The number of students with gray eyes and brown hair, is 5. That's because if we go to the table and look at the rows and columns, 5 is the number which relations these two facts.
- The difference of the number of students with gray eyes and brown hair and the number of students with green eyes and black hair is:
- Green eyes and black hair - gray eyes and brown hair
=> 11 - 5, which is 6.
Reshanda bought 17 plants to arrange along the border of her garden. How many distinct arrangements can she make if the plants are comprised of 6 tulips, 5 roses, and 6 daisies?
Given the word problem, we can deduce the following information:
1. Reshanda bought 17 plants to arrange along the border of her garden.
2. The plants are comprised of 6 tulips, 5 roses, and 6 daisies.
To determine the distinct arrangements that can she make, we use permutation as it an arrangement of objects in a definite order. The process is shown below:
[tex]Arrangements=\frac{n!}{p_1!p_2!p_3!}[/tex]where:
n=number of different objects=17
p1=objects of the first kind=6
p2=objects of the second kind=5
p3=objects of the third kind=6
We plug in what we know:
[tex]\begin{gathered} Arrangements=\frac{n!}{(p_{1})!(p_{2})!(p_{3})!} \\ =\frac{17!}{6!5!6!} \\ Calculate \\ Arrangements=5717712 \end{gathered}[/tex]Therefore, the answer is 5717712 arrangements.
Which group of relatives make 25% of her guest she has 12 cousins 6 aunts 4 brothers 2 sister
From the statement of the problem, we know that the organizer has the following guests:
• 12 cousins,
,• 6 aunts,
,• 4 brothers,
,• 2 sisters.
The total number of guests is 12 + 6 + 4 + 2 = 24. A 25% of the total number of guests is 0.25*24 = 6 guests. Because the group of aunts has 6 members, that group represent 25% of her guest.
Answer
The group of 6 aunts represents 25% of her guests.
I need help with this practice I believe the subject for this is complex numbers and vectors I will send you an additional picture that goes along with this, it is a graph, use the graph to answer
Solution
- In order to plot these vectors using Parallelogram law, we need to write them in rectangular form i.e. in terms of the x and y-components.
- This is done below:
[tex]\begin{gathered} \vec{a}=-3i-5j \\ \vec{b}=i+4j \end{gathered}[/tex]- We can then proceed to plot the vectors on a graph.
- For vector a, the line of magnitude extends from the origin (0, 0) to the point (-3, -5) while the line of the magnitude of vector b extends from the origin (0, 0) to the point (1, 4).
- This is shown below:
- The vector addition of both vectors is given below:
[tex]\begin{gathered} \vec{a}+\vec{b}=-3i-5j+(i+4j) \\ \text{ Add only magnitudes of the same component} \\ \vec{a}+\vec{b}=-3i+i-5j+4j \\ \\ \therefore\vec{a}+\vec{b}=-2i-j \end{gathered}[/tex]- This implies that the vector addition of both vectors extends from the origin (0,0) to the point (-2, -1)
- This is depicted below:
My I please get help with this math. I need help answering for each of them
An angle measures 24.6° more than the measure of its complementary angle. What is the measure of each angle? _and_
You have two angles, let's call them ∠1 and ∠2 of unknown measure, one of them measures 24.6º more than the other and both angles are complementary.
Let "xº" be the measure of ∠1, then ∠2 will beasure (x+24.6)º
∠1 and ∠2 are complementar, this means that together they add up to 90º
[tex]\angle1+\angle2=90º[/tex]Replace the expression with the angles measures
[tex]x+(x+24.6)=90[/tex]And solve for x
[tex]\begin{gathered} 2x+24.6=90 \\ 2x=90-24.6 \\ 2x=63.6 \\ \frac{2x}{2}=\frac{65.4}{2} \\ x=32.7 \end{gathered}[/tex]The angles measure:
∠1=32.7º
∠2=32.7+24.6=57.3º
compute the unit rate. round to the nearest hundredth. 226 Miles on 12 gallons
The unit rate of miles per gallon is computed dividing the number of miles and the number of gallons as follows:
[tex]\frac{226\text{ miles}}{12\text{ gallons}}=18.83\frac{\text{miles}}{\text{gallon}}[/tex]MVT of a function x^2-6x+8 on (0,8)
According to the Mean Value Theorem:
[tex]f^{\prime}(c)\text{ = }\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex][tex]f^{\prime}(c)\text{ = }\frac{f(8)-f(0)}{8-0}[/tex]f(x) = x² - 6x + 8
f(0) = 0² - 6(0) + 8
f(0) = 8
f(8) = 8² - 6(8) + 8
f(8) = 64 - 48 + 8
f(8) = 24
f'(x) = 2x - 6
f'(c) = 2c - 6
[tex]\begin{gathered} 2c\text{ - 6 = }\frac{24-8}{8} \\ 2c\text{ - 6 = }\frac{16}{8} \\ 2c\text{ - 6 = 2} \\ 2c\text{ = 2 + 6} \\ 2c\text{ = 8} \\ c\text{ = }\frac{8}{2} \\ c\text{ = 4} \end{gathered}[/tex]1 of 9Place and label the following numbers on the number line.175-1.75Line Reader help me .
Ok, so:
We're going to place and label the following numbers on the number line.
-1
1.75
-1.75
-2
-2 1/2 = -3/2
-5/2
9/4
Lindan just received a dozen roses for her birthday. For the flowers, she fills up a rectangular vase with water. The vase has a square bottom that is 3 inches in width. The base stands 12 inches tall. There is a sponge filling the bottom of the vase for the flower stands. It is 4 inches tall. How much space is left in the vase with for flowers?
Volume of the vase = 3 x 3 x 12 = 108 in^2
Volume of the sponge = 3 x 3 x 4 = 36 in^2
Volume left = 108 - 36 = 72 in^2