The 49th term of the Arithmetic Progression is -266.
The given sequence is 70,63, 56, 49,..
The given sequence is in Arithmetic Progression,
Where,
a = first term = 70,
d = common difference = 63 - 70 = -7
The general term of Arithmetic Progression is given by
[tex]a_{n} = a +(n-1)d[/tex]
Now, for n =49, the term of A.P. will be
[tex]a_{49}[/tex] = 70 + (49 -1)*(-7)
= 70 + 48*(-7)
= 70 - 336
= - 266
Hence, The 49th term of the Arithmetic Progression is -266.
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Given: The base of the pyramid is a regular pentagon.13 ft5 ftWhat is the lateral area of the pyramid?O 100108.3O 150O162.5
The Solution.
The lateral area of the given pyramid is the total area of the 5 triangular faces of the pyramid.
So, we have
[tex]\text{Lateral Area of the pyramid = 5(}\frac{1}{2}bh)[/tex]In this case,
[tex]b=5\text{ ft, h=13 ft}[/tex]Substituting these values in the formula above, we get
[tex]\text{Lateral Area of the pyramid = 5}\times\frac{1}{2}\times5\times13[/tex][tex]\text{Lateral Area of the pyramid = }\frac{25\times13}{2}=\frac{325}{2}=162.5ft^2[/tex]Hence, the correct answer is 162.5 square feet (option 4).
ctice 3.4.PS-19 Use the expression 6.5u - (10 =2) + 13 to answer 9–10. 9. Which part of the expression represents a quotient? Describe its parts. 10. Which part of the expression represents a product of two factors? Describe its p 9. The part of the expression that represents a quotient is (10=2). (Use the operation symbols in the math palette as needed. Do not simplify.) In this quotient, 6 is the dividend and 5U is the divisor
10 is the dividend while 2 is the divisor
Here, from the part that represents the quotient, we want to get the divisor and the dividend
From the question, the part that represents a quotient is given as;
[tex]\frac{10}{2}[/tex]Now, when we speak of the dividend, we mean the numerator of the fraction, and when we talk of the divisor, we are talking about the denominator
In simpler terms, what we want to divide is the dividend while what we are dividing with is the divisor
With respect to the given question, 10 is the dividend while 2 is the divisor
a is the midpoint of segment XY.find the value of x and the length of XY
ANSWER
x = 3, XY = 18
EXPLANATION
We have that A is the midpoint of XY. It means that A divides XY into 2 equal parts.
This means that:
XA = AY
We have that:
XA = 3x
AY = 5x - 6
=> 3x = 5x - 6
Collect like terms:
3x - 5x = -6
-2x = -6
Divide through by -2:
x = -6 / -2
x = 3
That is the value of x.
Since A is the midpoint of XY and XA = AY, then:
XY = 2XA or XAY
So:
XY = 2XA
XY = 2 * 3x = 2 * 3(3)
XY = 2 * 9
XY = 18
That is the value of XY.
5. Jim owns a farm that has been passed down through his family. The taxassessment on his farm is $399,000. The local tax rate is $6.01 per $100 of theassessment. What is Jim's annual property tax?
Given:
The assessment value = $399,000.
The local tax rate is $6.01 per $100 of the assessment.
Required:
We need to find the annual property tax.
Explanation:
[tex]A\text{nnual property tax = }\frac{\text{\$6.01}}{100}\times\text{the assessment value}[/tex][tex]A\text{nnual property tax = }\frac{\text{\$6.01}}{100}\times399000[/tex][tex]A\text{nnual property tax = \$23979.90.}[/tex]Final answer:
[tex]A\text{nnual property tax = \$23,979.90.}[/tex]The following picture has the question that has me troubled can you show me how to get to the answer
Given that:
[tex]f(x)=\sqrt[]{x},x_0=8,dx=0.07[/tex]Find the change.
[tex]\begin{gathered} \nabla f=f(8+\text{0}.07)-f(8) \\ =f(8.07)-f(8) \\ =\sqrt[]{8.07}-\sqrt[]{8} \\ =0.0123474175 \end{gathered}[/tex]Find the estimate value.
[tex]\begin{gathered} df=\frac{1}{2\sqrt[]{8}}\cdot0.07 \\ =0.0123743687 \end{gathered}[/tex]Determine the approximate error.
[tex]\begin{gathered} |\nabla f-df|=|0.0123474175-0.0123743687| \\ =0.0000269512 \\ \approx0.00002 \end{gathered}[/tex]Option B is correct.
Help please I want to know how to solve this not just the answer!!
Answer:
20 overtime hours
Step-by-step explanation:
overtime starts at 40 hours anything after that would be considered overtime
After a dilation with center (0,0), the image of DB is D'B'. IDB = 4.5 and D'B' = 18, the scale factor of this dilation is (1) (3) (2) 5 (4) 4
We can write the length of DB like this:
[tex]4.5=\frac{9}{2}[/tex]Now, to find the scale factor of the dilation, we have to solve for k the following equation:
[tex]\frac{9}{2}k=18[/tex]then, we have the following:
[tex]\begin{gathered} \frac{9}{2}k=18 \\ \Rightarrow9k=18\cdot2=36 \\ \Rightarrow k=\frac{36}{9}=4 \\ k=4 \end{gathered}[/tex]therefore, the scale factor is k=4
Complete all of the following steps to for each problem below.Write C for combine (add) or D for difference (D)Write (+) if the sum will be positive or (-) if the sum will be negativeDetermine the final answer8 + -2 = -9 + -12 = -35 + 25 = -19 + 40 =
Answer:
+6
Step-by-step explanation:
We have to solve the following expression:
8 + (-2)
The + sign before the parenthesis means that the signal of the terms inside the parenthesis stay the same. So
8 + (-2) = 8 - 2 = +6
The answer is +6.
What is the solution to the inequality 2-2x > -20
To determine the solution for the given inequality, you have to solve it for x:
[tex]2-2x>-20[/tex]First, pass 2 to the right side of the inequality by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 2-2-2x>-20-2 \\ -2x>-22 \end{gathered}[/tex]Next, note that the x-term is multiplied by "-2", to reach the value of x you have to cancel the said multiplication. For this, you have to divide both sides of the expression by "-2"
Now, keep in mind, that when you divide or multiply an inequality by a negative number, the direction of the inequality gets inversed. This means that the symbol "greater than, >" will tur into the symbol "less than. <":
[tex]\begin{gathered} -\frac{2x}{-2}<-\frac{22}{-2} \\ x<11 \end{gathered}[/tex]The solution for this inequality will be the values of x less than 11, symbolically: x < 11
(1 4/7)_____-(15/21)
(1 4/7)
_____
-(15/21)
To solve;
we will cange the division to multiplication. By doing that 15/21 becomes 21/15
That is;
[tex]\frac{14}{7}\times-\frac{21}{15}[/tex]7 can divide 21 to give 3
Hence;
[tex]\frac{14}{1}\times-\frac{3}{15}[/tex]3 can also divide 15 to give 5
[tex]\frac{14}{1}\times-\frac{1}{5}[/tex]we will now multiply
[tex]=\frac{-14}{5}[/tex][tex]=-2\frac{4}{5}[/tex]Write the equation in equivalent exponential form.log (1) base 6 = 0The equivalent exponential form is(Type an equation.)
Answer
The equivalent exponential form is 6⁰ = 1
Explanation
Given:
[tex]\log_61=0[/tex]Solution:
Using the definition of a logarithm:
[tex]\begin{gathered} \log_bx=y \\ \\ \Rightarrow b^y=x \end{gathered}[/tex]Thus, the given equation in equivalent exponential form is
[tex]\begin{gathered} \log_61=0 \\ \\ \Rightarrow6^0=1 \end{gathered}[/tex]The equivalent exponential form is 6⁰ = 1
Which of the following points lies on the graph pf the equation 2x + 6y = 6?A. (-3, 0)B. (-2, 9)C. (-3, 2)D. (2, 6)
Answer:
[tex]C[/tex]Explanation:
Here, we want to get the point that lies on the given graph
To get this, if we substitute the x value and y value into the function, we should get the value on the right-hand side of the equation, which is 6
Let us look at the 3rd option:
[tex]2(-3)\text{ + 6\lparen2\rparen = -6 + 12 = 6}[/tex]From what we can see here, the random choice was correct and thus, C is the correct answer
In a case where this was incorrect, we simply substitute another point and continue this until we arrive at the correct answer choice
AT"U"V is the translation of AT"U"V. what is the translation rule? ("A" is actually a triangle)
we know that
The coordinate of point U is (-7,8) see the image
The coordinate of point U' is (7,0) see the image
so
The rule of the trnslation is 14 units to the right and 8 units down
therefore
the rule is
(x,y) ------> (x+14,y-8)Please get help with this for I have tried many times to get the correct answers for each but still could not
A dilation of a point with a factor k is given by:
[tex](x,y)\rightarrow(kx,ky)[/tex]In this case the dilation factor is ; which means that we need to multiply each component of the vertexes by two. After doing this we get the following graph for the original and final polygon:
From the figure we can answer the questions.
a)
Longest side length of the original figrue: 3 units
Longest side lenght of the final figure: 6 units.
b)
Longest side length of the final figure = 2 x Longest side length of the original figure.
c)
For a positive scale final figure is always bigger than the original one, therefore, the stament is False.
d)
Any dilation creates a similar figure since we are not changing the angles, only the lengths. Therefore the statement is True
Drag and drop the angles and line segments into the correct category to identify those that are chords, Inscribed angles, and central angles in the figure. The center of the circle is C. C E F DEF EF DCF DE Chords Inscribed Angles Central Angles
Given data:
The given figure is shown.
The chords are,
EF
DE
The inscribed angle is ∠DEF.
The central angle is ∠DCF.
Thus, EF and DE are chords. ∠DEF is inscribed angle, and ∠DCF is cenral angle.
Caitlin read a book. She started reading at 9:45 a.m. and ended at 10:37 a.m. How did How many minutes did Caitlin read?
To calculate the number of minutes, we have to convert the hours to minutes or we can calculate the difference between the starting and ending times to a fixed hour.
In this case, we will use the second approach.
We will use 10:00 am as the fixed hour.
Then, if she started reading at 9:45 am, 15 minutes had passed until 10 am.
If she ended reading at 10:37 am, 37 minutes passed from 10 am.
Then, we can add the two segments:
[tex]T=15+37=52\min [/tex]Answer: she read 52 minutes.
A laptop has ablisted price of $739.98 befire tax. If the sales tax rate is 8.75%, find the total cost of the laptop with sales tax included.
Total cost of laptop after sales tax is included = $804.73
Explanation:
price before sales tax = $739.98
Sales tax rate = 8.75%
Total cost of laptop after sales tax = $739.98 × (100% + 8.75%)
= $739.98 × (1 + 0.0875)
= 739.98 × 1.0875
= $804.73
Total cost of laptop after sales tax is included= $804.73
the cone has a diameter of 10.5 inches and height of 6.75 inches. what is the volume of the cone? (hundredths place)the ball has a diameter of 8 1/2inches what Is the volume of the sphere? (hundredths place)the difference between the two volumes is(round to the nearest hundredth)
where,
r is the base radius of the cone
h is the perpendicular height of the cone
In this case,
r = 10.5 / 2= 5.25in
h = 6.75in
[tex]\begin{gathered} \text{Therefore} \\ \text{volume of cone}=\frac{\pi\times5.25^2\times6.75}{3}=194.83in^3 \end{gathered}[/tex]Volume of a ball is given by
[tex]\text{volume of ball =}\frac{4}{3}\times\pi\times r^3[/tex]where r is the radius of the ball
in this case,
[tex]r=\frac{8\frac{1}{2}}{2}=4.25in[/tex]Therefore
[tex]\text{Volume of ball = }\frac{4\times\pi\times4.25^3}{3}=321.56in^3[/tex][tex]\begin{gathered} \text{The difference betw}een\text{ the two volumes=321.56-194.83}=126.73 \\ =126.73in^3 \end{gathered}[/tex]The figure is rotated 360° clockwise with the origin as the center of rotation. Which graph represents the rotated figure?
Given
The figure is rotated 360° clockwise with the origin as the center of rotation. Which graph represents the rotated figure?
Answer
After the rotation of 360 degrees, a figure comes back to original position
Option A is correct
Hope earns $12.35 an hour plus time and a half for weekend work. Last week she worked her regular 45 hours plus 16 hours of overtime on the weekend.What was her total pay for the week?
Answer:
$852.23
Explanation:
Given the hourly rate as $12.35, let's go ahead and determine what Hope earns per hour for weekend work as seen below;
Time and a half rate (Overtime rate) = 1.5 x 12.35 = $18.53
So if Hope worked her regular 45 hours plus 16 hours of overtime on the weekend, we can go ahead and determine her total pay as seen below;
Total pay = Regular wages + Overtime Wages
= (12.35 x 45) + (18.53 x 16)
= 555.75 + 296.48
= $852.23
Suppose that you are headed toward a plateau 25.1 meters high. If the angle of elevation to the top of the plateau is 16.5, how far are you from the base of the plateau? meters (Round your answer to the nearest tenth.)
Suppose that you are headed toward a plateau 25.1 meters high. If the angle of elevation to the top of the plateau is 16.5, how far are you from the base of the plateau? meters (Round your answer to the nearest tenth.)
we have that
tan(16.5)=25.1/x
x is the missing distance
solve for x
x=25.1/tan(16.5)
x=84.7 m
the answer is 84.7 metersWhat is the measure of angle B in this triangle?
Enter your answer in the box.
Answer:
Step-by-step explanation:
First, you add the degrees available to you, next, you need to count the variable and add them together, in this case, your problem should show, 40+20-30 for your degrees, which is 30 degrees. Next, you have an "x" and a "2x," therefore you add them together to get 3x. After doing this, you get to your 2-step equation, which should look like 30 + 3x = 180. You get 180 because that is the length of the triangle, it should always be 180. You can now start by subtracting 180 - 30, we switch the + and - when doing the first part. Now, you should have gotten, 150, with 150 you can divide it by 3, you divided by 3 because you switch the division and the multiplication, now you do 150 divided by 3, which is 50. YOUR ANSWER IS: x = 50.
you own 5 pairs of jeans and want to take 2 of them on vacation with you. in how many ways can you choose 2 pairs of jeans
SOLUTION:
Step 1:
In the question, we are given the following:
you own 5 pairs of jeans and want to take 2 of them on vacation with you.
In how many ways can you choose 2 pairs of jeans?
Step 2:
The details of the solution are as follows:
From this question, we can see clearly that this is an application of selection under combinatorial analysis:
[tex]n\text{ C}_r=\text{ }\frac{n!}{r!(\text{ n - r \rparen}!}[/tex][tex]\begin{gathered} Now\text{, we have that:} \\ \text{n = 5} \\ \text{r = 2.} \\ Then,\text{ we have that:} \\ 5\text{ C}_2\text{ = }\frac{5!}{2!\text{ \lparen 5- 2\rparen}!}=\text{ }\frac{5!}{2!3!}=\frac{5\text{ x 4 x 3}!}{2!\text{ x 3}!}=\frac{20}{2}=\text{ 10 ways} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]10\text{ ways}[/tex]
This is the last question we have been stuck on it is there anyway you can help us out
Clearly,
[tex]1.3\cdot10^{12}[/tex]Is the largest number.
That's because it has more zeros due to its exponent is the most bigger of the four options.
Pls help!!!! asapppp
The percentage decrease in the price of the stock is 0.72%
The initial price of the technology stock = $9.66
The new price of the technology stock = $9.59
The decrease in price = The initial price of the technology stock - The new price of the technology stock
Substitute the values in the equation
= 9.66 - 9.59
Subtract the terms
= $0.07
The percentage of decrease in price = (The decrease in price / The initial price of the technology stock) × 100
Substitute the values in the equation
= (0.07 / 9.66) × 100
= 0.72 %
Hence, the percentage decrease in the price of the stock is 0.72%
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6×(11_6)÷2= do get this
Ayden, remember the order of operations PEMDAS.
1. Solve the Parentheses First
2. Solve the Exponents
3. Solve the Multiplication and Division
4. Finally, solve the Addition and Subtraction
Solving our exercise, we have:
6× (11 - 6) ÷ 2 =
6 x 5 / 2 =
30/2 =
Congratulations, Ayden! You did it!
3(4x+3)-12how do you simplify
By following the order of operations, we need to evaluate first the multiplication of 3 and (4x+3) by using the distributive property.
[tex]\begin{gathered} 3(4x+3)-12\text{ (given)} \\ \\ \text{apply the distributive property} \\ =(3\cdot4x+3\cdot3)-12 \\ =12x+9-12 \end{gathered}[/tex]After that, combine like terms, we see from the previous solution that 12x has no other like terms, and it will remain as is. 9 and 12 however are both constant, and should be simplified
[tex]\begin{gathered} 12x+9-12 \\ =12x-3 \end{gathered}[/tex]Therefore, 3(4x+3) - 12, when simplified is 12x - 3.
An investor invested a total of 57000 into two bonds. One bond paid 3% simple interest, and the other paid 2 7/8% interest. The investor earned a total of $1676.25 in annual interest. How much was originally invested in each account?
Answer:
$30,000 (at 3%) and $27,000 (at 2 7/8%)
Explanation:
The investor invested a total of 57000
• Let the amount invested at 3% simple interest = x
,• Then, the amount invested at 2 7/8% simple interest = 57000-x
Recall the formula for simple interest:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]Interest at 3%
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{x\times3\times1}{100} \\ =\frac{3x}{100} \\ =0.03x \end{gathered}[/tex]Interest at 2 7/8%
[tex]\begin{gathered} SI=\frac{(57000-x)\times2\frac{7}{8}\times1}{100} \\ =\frac{2.875(57000-x)}{100} \\ =0.02875(57000-x) \end{gathered}[/tex]Total Interest
The investor earned a total of $1676.25 in annual interest. Therefore:
[tex]\begin{gathered} 0.03x+0.02875(57000-x)=1676.25 \\ 0.03x+1638.75-0.02875x=1676.25 \\ 0.03x-0.02875x=1676.25-1638.75 \\ 0.00125x=37.5 \\ x=\frac{37.5}{0.00125} \\ x=30,000 \end{gathered}[/tex]Thus, the amount invested at 3% simple interest = $30,000
The amount invested at 2 7/8% simple interest = 57,000-30,000 = $27,000
2) Elena has some bottles of water that each holds 17 fluid ounces. a) Write an equation that relates the number of bottles of water (b) to the total volume of water (w) in fluid ounces. b) How much water is in 51 bottles? Show your work. c) How many bottles does it take to hold 51 fluid ounces of water? Show your work.
Answer:
(a)
Since each bottle holds 17 fluid ounces, then if b is the number of bottles of water and w is the total volume of water in fluid ounces we can set the following equation:
[tex]w=17b\text{.}[/tex](b)
Now, if b=51,
[tex]w=17\times51=867.[/tex]Therefore, in 51 bottles there are 867 fluid ounces.
(c)
If w=51, solving for b we get:
[tex]\begin{gathered} 51=17b, \\ \frac{51}{17}=b, \\ b=3. \end{gathered}[/tex]
Therefore, it would take 3 bottles to hold 51 fluid ounces.
A blimp provides aerial television views of a tennis game. The television camera sights the stadium at 14° angle of depression. The altitude of the blimp is 300m . What is the line-of sight distance from the television camera to the base of the stadium ? Round to the nearest hundred meters.
Notice that with the information given, we can make a simple schematics of a right angle triangle for which we know an acute angle, a leg, and are asked to find the other leg of the triangle (or the hypotenuse, since the word "line of sight is not used properly in the text of the problem). The schematics is shown below:
The other leg of the right triangle is pictured in red in the image, if it is what the problem is asking (LINE OF SIGHT DISTANCE, which is always understood as a horizontal reference).
So we can use the tangent function to solve this case, as shown below
[tex]\begin{gathered} \tan (14\circ)=\frac{300}{d} \\ d=\frac{300}{\tan (14)}\approx1203.23 \end{gathered}[/tex]which tells us that the horizontal distance between camera and end of the field is approximately 1203.23 meters.
In the case that the problem is asking for the slant distance between the camera and the end of the field, we need to find the HYPOTENUSE of the right angle triangle (pictured in orange in the image above), and in such case we use the sine function as shown below:
[tex]\begin{gathered} \sin (14)=\frac{300}{\text{hyp}} \\ \text{hyp}=\frac{300}{\sin (14)}\approx1240.07 \end{gathered}[/tex]Which tells us that the slant distance between camera and the end of the field is about 1240.7 meters
From the drawing you sent, it looks more like the teacher may be asking for the slant distance. So please use the second answer : 1240.7 meters.
Please remind you teacher that the standard use of "line of sight" is to represent the horizontal line from which the angle of elevation or angle of depression is measured. So it is not appropriate to use the term in the context it has been used.