The given sequence are:
2, 4, 8, 16...
Here, first term(a) = 2, common ratio(r) = 2 and we find the 25th term.
Therefore, we know that the sequence formula is:
[tex]a_r=ar^{n-1}[/tex]Then, for the 25th term:
[tex]a_{25}=2\times2^{25-1}=2\times2^{24}=33554432[/tex]Total money in dollars:
[tex]33554432\times0.01=335544.32[/tex]Answer: the girl will have $335544.32
Rewrite the following equation in logarithmic form using a base 10 logarithm.Use log for the base 10 logarithma = 10^K
we have the expression
[tex]a=10^k[/tex]Applying log both sides
[tex]\begin{gathered} \log _{10}a=\log _{10}10^k \\ \log _{10}a=k\cdot\log _{10}10^{} \\ \log _{10}a=k\cdot1 \\ k=\log _{10}a^{} \end{gathered}[/tex]Let f (x) = 8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down. What is the equation for g(x)? Enter your answer in the box.
ANSWER
[tex]g(x)=32x-7[/tex]EXPLANATION
We want to find the equation for g(x).
First, the function is stretched vertically by a factor of 4. This means that the function changes as follows:
[tex]f(x)\to4f(x)[/tex]Therefore, the function becomes:
[tex]\begin{gathered} 4(8x) \\ \Rightarrow32x \end{gathered}[/tex]Then, it is translated 7 units down. This means that the function changes as follows:
[tex]f(x)\to f(x)-7[/tex]Therefore, the equation for g(x) is:
[tex]g(x)=32x-7[/tex]Lauren made a large compost bin in her back yard. What is the volume of the compostbin?
Answer:
1365 ft^3
Explanation:
The compost bin can be thought of as being formed of two boxes.
The volume of the front box is
[tex](7ft)(21ft)(5ft)=735ft^3[/tex]And the volume of the box at the end is
[tex](3ft)((3+7)ft)(21ft)=630ft^3[/tex]Hence, the volume of the compost bin is the sum of the volumes above.
[tex]\begin{gathered} V=735ft^3+630ft^3 \\ V=1365ft^3 \end{gathered}[/tex]The volume of the compost bin is 1365ft^3.
What does the constant 0.935 reveal about the rate of change of the quantity?
The given constant is 0.935.
The constant 0.935 is less than 1, so it represents a DECAY.
Subtract the constant from 1 to get the decay rate:
[tex]1-0.935=0.065=0.065\times100\%=6.5\%[/tex]The unit of t is hours.
The exponent is t/24.
The reciprocal is 24.
The time frame of rate: 24 hours
This is equivalent to a day.
Hence, the complete statement is:
The function is decaying exponentially at a rate of 6.5% every day.
please help me with this assignment On a piece of paper graph y-5>2x-10. Then determine which answer choice matches the graph you drew.
The given function is,
[tex]\begin{gathered} y-5>2x-10 \\ 2x-y<5 \\ \end{gathered}[/tex]So, let us take the point, (3,1)
[tex]2\times3-1<5[/tex]is not true
Therefore, graph D is true
In the diagram below of triangle ABC, D is a midpoint of AB and E is a midpoint of BC. If mZDEB = 119 - 7x, and mZACE = 101 - 5x, what is the measure of ZACE? B D E A С
We want to find the measure of the ∠ACE. For doing so, we are going to use some geometrical properties with the information given.
As D is the midpoint of AB, we have that:
[tex]AD\cong DB[/tex]And as E is the midpoint of BC, we have:
[tex]BE\cong EC[/tex]Moreso, we can say that:
[tex]\frac{AB}{DB}=\frac{BC}{BE}=2[/tex]And thus, the sides are proportional. As both triangles have the angle:
[tex]\angle DBE\text{ which is the same as }\angle ABC[/tex]We can say that the triangles ABC and DBE are similar by the Theorem SAS (side-angle-side):
[tex]\begin{gathered} \text{Side 1: }AB\approx DB \\ \text{Angle: }\angle DBE \\ \text{Side 2: }CB\approx EB \end{gathered}[/tex]Thus, their sides are proportional, and their corresponding angles are congruent.
As the angles ACE and DEB are corresponding (on the two triangles), they have the same measure:
[tex]\begin{gathered} m\angle ACE=m\angle DEB \\ 101-5x=119-7x \\ \text{And we solve for x:} \\ 101-5x+7x=119-7x+7x \\ 101+2x=119 \\ 2x=119-101 \\ 2x=18 \\ x=\frac{18}{2}=9 \end{gathered}[/tex]This means that the value of x is 9. Now, replacing on the value of ACE, and we get:
[tex]\begin{gathered} m\angle ACE=101-5x \\ =101-5(9) \\ =101-45 \\ =56 \end{gathered}[/tex]Thus, the value of the angle ∠ACE is 56°.
Write an equation in standard form of the line that passes through the point and has thegiven slope.(-2, 4); m = -6None of the other answers are correctOy - 6x = 86x + y = -8Oy - 6x = -86x - y = 8
the general form of the line is
[tex]y=mx+b[/tex]where m is the slope of the line and b the y-intercept
we get the slope from the statement m=-6
[tex]y=-6x+b[/tex]now to find the value of b we replace the point (-2,4) and solve for b
[tex]\begin{gathered} (4)=-6(-2)+b \\ 4=12+b \\ b=4-12 \\ b=-8 \end{gathered}[/tex]now replace the value of b
[tex]y=-6x-8[/tex]and transform to the standard form placing the unknows on the same side
[tex]y+6x=-8[/tex]we can reorganize
[tex]6x+y=-8[/tex]then right option is Third option
Math 8th grander, please help us
The first thing we have to see is that exercise (c) is given as follows
[tex](c)_{}\to\frac{-4}{f(k)}[/tex]From (e) we know:
[tex]f(k)=-4k+7[/tex]So we replace f(k) of the (e) part on the (c) part as follows:
[tex]f(k)=\frac{-4}{(-4k+7)}[/tex]Now we must find the value of x the function F (k) is not defined. This value is given when the denominator of the function gives 0 since the function would be indeterminate then:
[tex]\begin{gathered} -4k+7=0 \\ -4k=-7 \\ k=\frac{7}{4} \end{gathered}[/tex]The domain of this function is indeterminate for k = 7/4 and this value is the one that must be excluded from the domainAll functions have a domain and a range. The domain of a function is all the values that the function can take along the k-axis and the range on the f(k)-axis.
Karen is 21 years older now than Oliver. In 4 years Karen will be double Oliver’s age. How old is each now ?
Let
x -----> Karen's age now
y ----> Oliver's age now
we have that
x=y+21 --------> equation 1
(x+4)=2(y+4) ---> equation 2
Solve the system of equations
Substitute equation 1 in equation 2
(y+21+4)=2(y+4)
solve for y
y+25=2y+8
2y-y=25-8
y=17
Find out the value of x
x=17+21
x=38
therefore
Karen is 38 years old nowOliver is 17 years old nowin the graph shown below, are lines L1 and L2 perpendicular? explain. choose the correct statement below A) no,the lines L1 and L2 are not perpendicular because the product of their slopes does not equal -1B)no, the lines L1 and L2 are not perpendicular because the products of their slope equals -1C) yes, the lines L1 and L2 are perpendicular because the products of their slope equals -1D)yes, the lines L1 and L2 are perpendicular because the product of their slope do not equal -1
In order to see if the lines are perpendicular, we must compute their slopes.
The slope formula for two points (x1,y1) and (x2,y2) is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For instance, if we take these points in the line L1
[tex]\begin{gathered} (x_1,y_1)=(-1,1) \\ (x_2,y_2)=(5,-2) \end{gathered}[/tex]and substitute their values into the slope formula, we obtain
[tex]\begin{gathered} m=\frac{-2-1}{5-(-1)} \\ m=\frac{-3}{5+1} \\ m=\frac{-3}{6} \\ m=-\frac{1}{2} \end{gathered}[/tex]Similarly, we must do the same for line L2. If we take these points in the line L2
[tex]\begin{gathered} (x_1,y_1)=(1,-4) \\ (x_2,y_2)=(7,5) \end{gathered}[/tex]and substitute their values into the slope formula, we have
[tex]\begin{gathered} M=\frac{5-(-4)}{7-1} \\ M=\frac{5+4}{6} \\ M=\frac{9}{6} \\ M=\frac{3}{2} \end{gathered}[/tex]Now, the perpendicular slope is the opposite reciprocal of the line to which it is perpendicular, that is
[tex]M=-\frac{1}{m}[/tex]must be fulfiled. Lets see if this occurs:
[tex]\begin{gathered} M=-\frac{1}{-\frac{1}{2}} \\ M=\frac{1}{\frac{1}{2}} \\ M=2 \end{gathered}[/tex]and we can see that 2 is not equal to 3/2. This imply that lines L1 and L2 are not perpendicular
I have answers to the questions but I'm not sure if there are right or not.
Answer with Explanation: Provided the following dot plot, we have to find the (1) Mean, (2) median, and the (3) mode:
(1) Mean:
[tex]\begin{gathered} M=\frac{a_1+a_2+a_3+...+a_N}{N} \\ \therefore\rightarrow \\ M=\frac{60}{22}=2.73 \end{gathered}[/tex](2) Median:
[tex]m=\frac{2.5+2.5}{2}=2.5[/tex](3) Mode:
[tex]\begin{gathered} \text{ Value that appears most often:} \\ mode=2.5\rightarrow\text{ Appears seven times.} \end{gathered}[/tex]Use 5 squares each with a side of 2 cm to make a shape that has a perimeter of 20 cm
Given:
Let us take 5 squares each with a side of 2 cm.
To make: The shape that has a perimeter of 20cm
Explanation:
Let us draw the shape as follows,
We know that the sum of all outer sides of the shape is the perimeter.
So, the perimeter of the above shape is 20.
Livi24 A teacher divided 60 stickers among 3 students in a ratio of 2:3:5. Howmany stickers did each student receive?
1st = 12 stickers
2nd = 18 stickers
3rd = 30 stickers
Explanation:Total stickers = 60
Ratio of the three students = 2:3:5
Let the ratio of the 1st student = 2
The ratio of the 2nd student = 3
The ratio of the 3rd student = 5
Total ratio = 2 + 3 + 5 = 10
[tex]\begin{gathered} \text{The amount each student gets = }\frac{ratio}{\text{total ratio}}\times\text{ total stickers} \\ \end{gathered}[/tex][tex]\begin{gathered} 1st\text{ student = }\frac{2}{10}\times60 \\ 1st\text{ student = 12 stickers} \end{gathered}[/tex][tex]\begin{gathered} 2nd\text{ student = }\frac{3}{10}\times60 \\ 2nd\text{ student = 18} \end{gathered}[/tex][tex]\begin{gathered} 3rd\text{ student = }\frac{5}{10}\times60 \\ 3rd\text{ student = }30\text{ stickers} \end{gathered}[/tex]Patrick purchased a new tires that were regularly priced at $92.99 each but are on sale for $20 off per tire. If the sales tax rate is 4% how much will be charged to Patrick’s Visa card??
Since the regular price is 92.99 for each tire, and it has a discount of 20, the final price of each tire is:
92.99 - 20 = 72.99
Now, since he bought 8 tires, the total cost would be:
8 * 72.99 = 583.92
We now need to include the sale tax rate of 4%. We can do so by using the following formula:
price + tax = (1 + tax rate) * price
So, we have:
price + tax = (1 + 4%) * 583.92
Notice that:
4% = 4/100 = 0.04
Then:
price + tax = (1 + 4%) * 583.92
= (1 + 0.04) * 583.92
= 1.04 * 583.92
= 607.2768
≅ 607.28
Therefore,
$607.28 will be charged to Patrick's VISA card.
wich shows how the distributive property can be used to evaluate 7×8 4/5
According to the given data we have the following expression:
7×8 4/5
In order to find out which shows how the distributive property can be used for we would have to make the following:
First convert mixed numbers to improper fraction
[tex]a\frac{b}{c}=\frac{a\cdot c+b}{c}[/tex][tex]\begin{gathered} So,\text{ }8\frac{4}{5}=\frac{8\times5+4}{5}=\frac{44}{5} \\ 7\times\frac{44}{5}=\frac{7\times\:44}{1\times\:5}\text{ by applying the fraction rule} \end{gathered}[/tex][tex]\begin{gathered} \text{Next, }\mathrm{Multiply\: the\: numbers\colon}\: 7\times\: 44=308 \\ =\frac{308}{1\times\:5} \\ \mathrm{Multiply\: the\: numbers\colon}\: 1\times\: 5=5 \\ =\frac{308}{5} \end{gathered}[/tex]Finally, convert the improper fraction to mixed number:
[tex]So,\text{ }\frac{308}{5}=61\frac{3}{5}[/tex]Therefore, the option that shows how the distributive property can be used to evaluate 7×8 4/5 would be the first option.
The graphs of f(x) and g(x) are shown below: What are the solutions to the equation f(x) = g(x)?
Fred's monthly salary is $ 5,625. 1. Use the lattice model to multiply 2. What is the Fred's annual salary? 3. Upload the assignment 1
Solution
For this case we can do the following:
then the final answer for this case is:
67500
Find the area of the shape below 8 yards 3 yards 3 yards 8 yards
The given shape is a rectangle with base 8 yards and height 3 yards.
The area of a rectangle is the product of its base and its height:
[tex]A=b\times h[/tex]Replace b = 8yd and h = 3yd to find the area of the rectangle:
[tex]A=(8yd)\times(3yd)=24yd^2[/tex]Therefore, the area of the shape is 24 square yards.
one black linen tablecloth is required for each of 54 tables at a banquet. there are only 12 black and 20 white linen tablecloths in the banquet hall storeroom. how many additional linens are neede?
A banquet is a formal, substantial dinner that a large group of people share. Banquets are typically conducted to boost a host's reputation or to strengthen social ties between co-contributors. These goals can be fulfilled today through events like ceremonies, celebrations, or charitable gatherings.
52 x 72 tablecloth for a 4 foot rectangle dinner table (standard Drop) 52 x 114-inch tablecloth (standard drop) and 90 x 132-inch tablecloth for a 6-foot rectangular dinner table (full drop).
What size tablecloths am I going to need?
Seating at Round Tables & Sizes of Linen
Size of the Table Seating Linen 6' x 30" 6-8 People 120" Round
8' x 30 "8 to 10 people
72" x 120" 90" x 156" \s108" "Round.
To learn more about Banquet refer to:
https://brainly.com/question/18943399
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Indigo Depot is having a clearance sale for the spring items all clearance items are marked an additional 35% off the sale price address that originally cost $130 before any discount is on sale for 20% off what is the final price round your answer to the nearest cent if necessary
Indigo Depot is having a clearance sale for the spring items all clearance items are marked an additional 35% off the sale price address that originally cost $130 before any discount is on sale for 20% off what is the final price round your answer to the nearest cent if necessary
step 1
originally cost $130
sale for 20%
100%-20%=80%=80/100=0.80
$130*0.80=$104 -----> sale price
step 2
all clearance items are marked an additional 35% off the sale price
100%-35%=65%=65/100=0.65
$104*0.65=$67.60
therefore
the final price is $67.60Find the slope between the two points: (-7, 4) and (-7, 9)
Answer:
slope is undefined
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 7, 4 ) and (x₂, y₂ ) = (- 7, 9 )
m = [tex]\frac{9-4}{-7-(-7)}[/tex] = [tex]\frac{5}{-7+7}[/tex] = [tex]\frac{5}{0}[/tex]
division by zero is undefined thus the slope is undefined
FShºD150RMFind the measure of ZDRE.
what is the value of f(-1)
Given:
To find f(1), all we need to do is to replace x by 1:
Therefore, f(1)=1.
Let p be "She is a tennis champion," and let q be "She is not very good." What statement is equivalent to the symbolic form p⟹∼q?Select the correct answer below:Her being a tennis champion implies that she is very good.Being a tennis champion is a necessary condition of being very good.If she is very good, then she is a tennis champion.She is a tennis champion only if she is very good
We know that
• p: She is a tennis champion.
,• q: She is not very good.
It's important to know that the connector ⟹ refers to an implication so if we have the statement p⟹q it's read as "if p then q". The symbol ∼ refers to the negation of a statement, for example, if q means "she is not very good" then ∼q means "she is very good", so the symbol ∼ can be seen as the opposite meaning.
So, in this case, we have the statement p⟹∼q, which is read as "if she is a tennis champion then she is very good.
Therefore, the correct answer would be Her being a tennis champion implies that she is very good.
The exponential function is an example of exponential growth. f(x) = 3x+2 Select one: True False A
Given:
The exponential function is an example of exponential growth
[tex]f(x)=3^{x+2}[/tex]Required:
To check whether the given statement is true or false.
Explanation:
Growth of a system in which the amount being added to the system is proportional to the amount already present.
Therefore the given statement is TRUE.
Final Answer:
[tex]f(x)=3^{x+2}[/tex]Is exponential function.
TRUE.
Select all the correct answers. Which three pairs of side lengths are possible measurements for the triangle? А 45° 45 B с AB=9V2. AC =18 BC = 10, AC = 102 AB=7. BC=7V3 BC = 10/3, AC = 20 AB=9, AC = 18 AB = 14. BC = 14
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The three pairs of side lengths that are possible measurements for the triangle is:
[tex]AB\text{ = 14 , BC = 14}[/tex]since the base angles of the triangle are equal with 45 degrees each and a vertical angle of 90 degrees.
If sin(x)=1/4 and sec(y)=5/3, where x and y lie between 0 and pi/2, evaluate sin(x+y)
The trigonometric identity sin(x+y) is given by the following formula:
[tex]\sin (x+y)=\sin x\cdot\cos y+\cos x\cdot\sin y[/tex]We need to find then cos(y), cos(x) and sin(y).
Other trigonometric identities we can use are:
[tex]\begin{gathered} \sec y=\frac{1}{\cos y}\text{ Identity (1)} \\ \sin ^2a+\cos ^2a=1\text{ Identity (2)} \end{gathered}[/tex]First, replace the sec(y) value and find cos(y):
[tex]\begin{gathered} \frac{5}{3}=\frac{1}{\cos y} \\ \therefore\cos y=\frac{1\times3}{5}=\frac{3}{5} \end{gathered}[/tex]Now, apply the second identity to find cos(x) and sin(y):
[tex]\begin{gathered} \sin ^2x+\cos ^2x=1 \\ \therefore\cos ^2x=1-\sin ^2x \\ \therefore\sqrt[]{\cos^2x}=\sqrt[]{1-\sin^2x} \\ \therefore\cos x=\sqrt[]{1-(\frac{1}{4})^2} \\ \cos x=\sqrt[]{1-\frac{1}{16}^{}}=\sqrt[]{\frac{1\cdot16-1\cdot1}{16}} \\ \cos x=\sqrt[]{\frac{15}{16}}=\frac{\sqrt[]{15}}{\sqrt[]{16}}=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]And now sin y=
[tex]\begin{gathered} \sin ^2y=1-\cos ^2y \\ \therefore\sin y=\sqrt[]{1-\cos ^2y} \\ \therefore\sin y=\sqrt[]{1-(\frac{3}{5})^2} \\ \sin y=\sqrt[]{1-\frac{9}{25}}=\sqrt[]{\frac{1\cdot25-1\cdot9}{25}} \\ \sin y=\sqrt[]{\frac{16}{25}}=\frac{\sqrt[]{16}}{\sqrt[]{25}}=\frac{4}{5} \end{gathered}[/tex]Now, replace these values into the identity sin(x+y) and solve as follows:
[tex]\begin{gathered} \sin (x+y)=\sin x\cdot\cos y+\cos x\cdot\sin y \\ \sin (x+y)=\frac{1}{4}\cdot\frac{3}{5}+\frac{\sqrt[]{15}}{4}\cdot\frac{4}{5} \\ \sin (x+y)=\frac{1\times3}{4\times5}+\frac{\sqrt[]{15}\times4}{4\times5} \\ \sin (x+y)=\frac{3}{20}+\frac{4\sqrt[]{15}}{20}=\frac{3+4\sqrt[]{15}}{20} \\ \sin (x+y)\approx0.925 \end{gathered}[/tex]Hello! This is the problem I am having a lot of problem with.I may warn you there is some rubbish so ignore it.
Surface Area of a Cube
A cube has 6 faces or surfaces, all of them have the same size and therefore, the same area.
The surface area of one of the faces is the area of a square of side length 9 ft:
[tex]A=(9\text{ ft})^2=81\text{ }ft^2[/tex]The total surface area is 6 times this area, thus:
[tex]\begin{gathered} SA=6\cdot81\text{ }ft^2 \\ SA=486\text{ }ft^2 \end{gathered}[/tex]which equation and solution correctly represents d the number of bundles of daisies Alexis purchased?
d represents the number of daises purchased.
She purchased 12 bumdles of tulips
If both types of flowers cost $4 per bundle, then the cost of both flowers is
4(d + 12)
If she spent $76 on flowers, then the correct equation would be
4(d + 12) = 76
Dividing both sides by 4, we have
d + 12 = 19
d = 19 - 12
d = 7
Option A is correct
13) Kyle has an indoor basketball court. The rectangular court has a perimeter of 120 feat. The length of the court is 14 feet longer than the width. Find the length and width of the court.
EXPLANATION:
-We must first know what data the exercise gives us.
-We must formulate the exercise based on the data we have, knowing that in the end the total value must be 120
-To find the width value we must work with an unknown or variable which in this case will be w.
-Since a rectangular court has two widths and two lengths, we propose the exercise as follows:
[tex]\begin{gathered} P=120\text{ L}=14\text{ feat }w=? \\ \text{widht}+widht+14+14=120 \\ 2w+28=120 \\ 2w=120-28 \\ 2w=92 \\ w=\frac{92}{2} \\ \textcolor{#FF7968}{w=46} \\ 46+46+14+14=120 \end{gathered}[/tex]