Answer:
D) [tex]S_{14} = 875[/tex].
Step-by-step explanation:
Given : If the first term of the series is 30 and the 14th term is 95,
To find : what is the sum of all the terms of the series.
Solution : We have given
First term = 30 .
14 th term = 95.
Sum of all term = [tex]S_{n} =\frac{n(first\ term +\ last\ term)}{2}[/tex].
Here, n = 14.
[tex]S_{14} =\frac{14(30 +95)}{2}[/tex].
[tex]S_{14} =\frac{14(125)}{2}[/tex].
[tex]S_{14} =\frac{1750}{2}[/tex].
[tex]S_{14} = 875[/tex].
Therefore, D) [tex]S_{14} = 875[/tex].
Answer:
The sum of all the terms in series is 875.
Step-by-step explanation:
Given : If the first term of the series is 30 and the 14th term is 95,
To find : What is the sum of all the terms of the series?
Solution :
The first term of the series is 30 i.e. a=30
The 14th term of series is 95 i.e. [tex]a_{14}=95[/tex]
We know that in arithmetic series the 14th term is defined as
[tex]a_{14}=a+13d[/tex]
Substitute the value of a,
[tex]95=30+13d[/tex]
[tex]95-30=13d[/tex]
[tex]65=13d[/tex]
[tex]d=\frac{65}{13}[/tex]
[tex]d=5[/tex]
The common difference is 5.
The sum of the series is given by,
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{14}=\frac{14}{2}[2(30)+(14-1)5][/tex]
[tex]S_{14}=7[60+(13)5][/tex]
[tex]S_{14}=7[60+65][/tex]
[tex]S_{14}=7[125][/tex]
[tex]S_{14}=875[/tex]
Therefore, The sum of all the terms in series is 875.
I need help with this question
ANSWER
Option D
EXPLANATION
The given function is
[tex]y = \sqrt{16x - 32} - 3[/tex]
We factor 16 under the radical.
[tex]y = \sqrt{16(x - 2)} - 3[/tex]
[tex]y = \sqrt{16} \times \sqrt{(x - 2)} - 3[/tex]
[tex]y = 4 \sqrt{x - 2} - 3[/tex]
This is the graph of
[tex]y = 4\sqrt{x } [/tex]
translated 2 units right and 3 units down.
The last option is the correct choice.
In a rectangle MPKN, the diagonals intersect each other at point O. A line segment OA is an altitude of a triangle MOP, and m∠AOP = 18°. Find the measure of ∠ONK.
To find the measure of ∠ONK in rectangle MPKN with given conditions, it's determined through the congruency of triangles and properties of a rectangle that ∠ONK is 72°.
The question involves finding the measure of ∠ONK in rectangle MPKN, where the diagonals intersect at point O, and a line segment OA is an altitude of triangle MOP with m∠AOP = 18°. Given the properties of a rectangle, we know that its diagonals bisect each other and are equal in length. Therefore, triangles MOP and NOP are congruent.
Because OA is the altitude to hypotenuse MP of triangle MOP, it creates two right triangles, OAM and OAP. The angle ∠AOP is given as 18°, which means ∠MOA = 90° - 18° = 72° since triangle OAM is a right-angled triangle. Because the diagonals of the rectangle bisect each other at O, triangle ONP is congruent to triangle OMP, and hence ∠ONK (which is also ∠ONP) is equal to 72° as angle ∠ONP is supplementary to ∠MOA in rectangle MPKN.
Which expression represents the number of ways that a president and vice president can be chosen out of a group of 15 people?
Answer: The answer is 15 * 14
Step-by-step explanation:
You start with 15 people to choose from to select a president, so you have 15. After removing one person 15-1,=14 you have fourteen people to choose from, to select a vice president. This gives you 15*14.
The expression that can be used to represent the number of ways that a president and a vice-president can be chosen out of a group of 15 people is 15×14 or ¹⁵P₂.
What is Permutation?Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
[tex]^nP_r = \dfrac{n!}{(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
The number of people that are available for the post of the president is 15, while the number of people that are available for the post of vice-president after the president is selected is 14. Therefore,
Number of ways in which president and vice-president can be selected
= ¹⁵P₂
= 15 × 14
Hence, the expression that can be used to represent the number of ways that a president and a vice-president can be chosen out of a group of 15 people is 15×14 or ¹⁵P₂.
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The price of a watch was increased by 20% to 198. What was the price before the increase?
To find the original price before the increase, divide the new price by 1 + the percent of increase.
198 / 1.20 = 165
The original price was $165
The price before the increase was $ 165
What is percentage?Percentage can be said as a part of a whole expressed in hundredths .
How to know what was the price of the watch before the increase?Let the price of the watch be $ x
According to the problem,
The price of a watch was increased by 20% to $ 198.So, we can write x + 20x/100 = 198
⇒ 6x/5 = 198
⇒ x = 165
∴ The price before the increase was $ 165
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26% of animals at the animals shelter are dogs. About what fraction of animals at the shelter are dogs
Answer:
The answer is 26/100
PLEASE HELPPPP i will give brainliest to whoever answers first please and thanks
The first term of a geometric sequence is 3, and the common ratio is 4. What is the 5th term of the sequence?
a) 768
b) 3,072
c) 192
d) 81
Answer: I got A. 768 as the answer
Which of the following points satisfies the inequality 2x - 3y < 1?
(-2, 1)
(, 0)
(2, -1)
I'm not sure about the second point you posted, but I believe the answer is (-2, 1). Here is my work:
Answer:-2,1
Step-by-step explanation:
What is the value of x?
Answer: Whats the whole question?
Step-by-step explanation:
The intersection of the prism and the plane is a _______
cross section.
Trapezoid
Rectangle
Square
Answer:
Rectangle
Step-by-step explanation:
The cross-section will result in a face, that looks just like the top face, since the cut + face are parallel. And because that face is rectangular, so will the cross-section.
Answer:
Rectangle
Step-by-step explanation:
Given : A prism and a plane
To Find : The intersection of the prism and the plane is a _______ cross section.
Solution:
We are given a rectangular prism
Let length be l , breadth be b and height be h
When the prism is intersected by plane , The height becomes 0 .
Length and breadth will remain same
So, the obtained figure is rectangle
So, Option B is true .
Hence The intersection of the prism and the plane is a rectangle cross section.
Which inequality represents the
following situation times 5 less
than a number is no more than 27?
[tex]\frac{3}{5}(x - 5) \leq 27[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: Option D
The inequality that represents the situation is:
[tex]\frac{3}{5}(x-5)\leq 27[/tex]
following situation
Step-by-step explanation:
Suppose an unknown number X.
That number minus 5 is:
[tex]x-5[/tex]
Now, [tex]\frac{3}{5}[/tex] times the unknown number minus 5 is:
[tex]\frac{3}{5}(x-5)[/tex]
We know that all this expression is not greater than 27.
Then we use the symbol "less or equal than" ([tex]\leq[/tex]) to represent the situation
[tex]\frac{3}{5}(x-5)\leq 27[/tex]
Weights of Andrews cats are 8 pounds, 15 pounds, 18 pounds, 15 pounds, and 12 pounds. Which statements are true about the weights of Andrews cats? Select the four that apply.
A. The mean is 13.6 pounds
B. The median is 16 pounds
C. The range is 10 pounds
D. The mode is 15 pounds
E. The mean is greater than the median
F. The median and the mode are the same
Answer:
a,b,d,f
Step-by-step explanation:
Subtract: (2x3+7x2−4)−(2x2+4x−10)
To subtract the given expressions, first, simplify each expression separately by combining like terms. Then subtract the second expression from the first expression by distributing a negative sign and adding it to the first expression.
Explanation:To subtract the given expressions, (2x^3+7x^2-4) - (2x^2+4x-10), we need to simplify each expression separately and then subtract them. First, combine like terms within each expression. Then, subtract the terms of the second expression from the first expression. This can be done by distributing a negative sign to each term in the second expression and then adding it to the first expression.
So, (2x^3+7x^2-4) - (2x^2+4x-10) = 2x^3+7x^2-4 - 2x^2-4x+10.
Combining like terms, we get 2x^3+(7x^2-2x^2)+(-4-4x)+(10). Simplifying further, we have 2x^3 + 5x^2 - 4x + 6. Therefore, the result of the subtraction is 2x^3 + 5x^2 - 4x + 6.
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(1) 1 UU
15. Line segment RW has endpoints R(4, 5) and W6, 20). Point P is
on RW such that RP:PW is 2:3. What are the coordinates of point P?
(1) (2,9) (2) (0, 11) (3) (2, 14) (4) (10,2)
14
Answer:
P = (4.8, 11)
Step-by-step explanation:
P = 3R + 2W
RP + PW
= 3(4,5) + 2(6,20)
2 + 3
= (12,15) + (12,40)
5
= (24,55) = (4.8, 11)
5
Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is
on RW such that RP: PW is 2:3. the coordinates of point P would be (0, 11).
What is the coordinate of the point which divides a line segment in a specified ratio?Suppose that there is a line segment {AB} such that a point P(x,y) lying on that line segment{AB} divides the line segment {AB} in m:n, then, the coordinates of the point P is given by:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
where we have:
the coordinate of A is (x_1, y_1)
and the coordinate of B is (x_2, y_2)
Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is
on RW such that RP: PW is 2:3.
[tex](x,y) = \left( \dfrac{2(6) + 3(-4)}{2+3} , \dfrac{2(20) + 3(5)}{2+3} \right)\\\\(x,y) = \left( \dfrac{12- 12}{5} , \dfrac{40+15}{5} \right)\\\\(x,y) = \left( \dfrac{0}{5} , \dfrac{55}{5} \right)\\\\(x,y) = (0, 11)[/tex]
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What is the mean of the set of data?
6, 7, 10, 12, 12, 13
6
7
10
11
Answer:
10
Step-by-step explanation:
Mean is all the given numbers in the set added together then divided by the total amount of numbers
6+7+10+12+12+13= 60
60÷6=10
Answer:10
Step-by-step explanation: Mean is all the given numbers in the set added together ,then divided by the total amount of numbers
6+7+10+12+12+13= 60
60÷6=10
the length is 4cm, the width is 3cm. find the area
547663
Step-by-step explanation:
Answer:
12 cm²
Step-by-step explanation:
To find the area of a rectangle, you multiply all of its dimensions together, which is length and width. That is A = l * w
Plug in: A = 4 cm * 3 cm
Multiply: A = 12 cm²
Solve for x
2(x+1)=8
Provide step by step instructions
Step-by-step explanation:
2 * (x + 1) = 8 | :2
x + 1 = 4 | -1
x = 3
Answer:
x = 3
Step-by-step explanation:
2 ( x + 1 ) = 8
⇒ Expand brackets
2 x + 2 = 8
⇒ Minus 2 from both sides
2 x = 6
⇒ Divide by 2 from both sides to isolate x
x = 3
Solve the equation for x.
the square root of the quantity x minus 6 end quantity plus 3 equals 10
A. x=1
B. x=13
C. x=43
D. x=55
ANSWER
D. x=55
EXPLANATION
The given radical equation is
[tex] \sqrt{x - 6} + 3 = 10[/tex]
Add -3 to both sides
[tex] \sqrt{x - 6} = 10 - 3[/tex]
[tex] \sqrt{x - 6} =7[/tex]
Square both sides.
[tex] { (\sqrt{x - 6})}^{2} = {7}^{2} [/tex]
[tex]x - 6 = 49[/tex]
Solve for x to get:
[tex]x = 49 + 6 = 55[/tex]
Example: 1, 6, 2, 3
Proportion is 1:2=3:6
25) 3, 6, 7, 14
Proportion is _________________
26) 2, 6, 5, 15
Proportion is _________________
27) 7, 2, 14, 4
Proportion is _________________
28) 2, 2, 1, 4
Proportion is _________________
29) 10, 5, 8, 4
Proportion is _________________
30) 3, 12, 8, 2
Proportion is _________________
25) proportion is 3:6=7:14
26) proportion is 2:6=5:15
27) proportion is 2:4=7:14
28) proportion is 1:2=2:4
29) proportion is 4:8=5:10
30) proportion is 2:8=3:12
which of the following best describes the word postulate
Answer:
Statements that are true with out any given proof
Step-by-step explanation:
There is no information needed for you to get your answer
Answer:
Statements that are true with out any given proof
Step-by-step explanation:
its basicly the def of it
please help me i dont get it at all
y = 218.2. The lenght of side y by trigonometry is 218.2.
In order to solve this problem we are going to use the angles and sides of a right triangle and its relation by expressions that we call trigonometric ratios.
In the image we can see that the lenght of the opposite leg is 141 , we do not know the lenght of the adjacent leg y and the hypotenuse x. The key to solve this problem is to use trigonometric ratios and the equation tan θ = sin θ/cos θ = opposite leg/adyacent leg = 141/y
Clear for y for the equation tan θ = sin θ/cos θ = 141/y, we obtain:
y = arctan θ (141)
y = arctan (43°)(141) = 218.2
Simplify the following expression log(x^4)-log(x^3)
Answer:
log x
Step-by-step explanation:
Using the rule of logarithms
• log [tex]x^{n}[/tex] ⇔ n log x
Hence
log [tex]x^{4}[/tex] - log x³
= 4 log x - 3 log x
=log x
The value of logx⁴ - logx³ will be logx.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
If you want to write 1 in logarithm then it will be log(base).
The first method →
Given,
⇒ logx⁴ - logx³
By log property that loga7 = 7loga
⇒ 4logx - 3 logx
⇒ logx
The second method →
This question can also be solved by another log property that
logm - logn = log(m/n)
Since given,
logx⁴ - logx³ = log(x⁴/x³) = logx
Hence, The value of logx⁴ - logx³ will be logx.
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if the diameter of a circle is 50 yards ,the radius is
If the diameter of a circle is 50 yards the radius must be 25 yards.
This is because the radius is always half the diameter of the circle. Since we know the diameter is 50 yards, half of 50 is 25 so the radius must be 25 yards.
Have a great day!
The radius of the circle is 25 yards.
What is a Circle ?A circle is a round shaped figure which has all its points in one plane and the distance between all the points on its circumference to the center of the circle is equal .
It is given that
Diameter of a circle is 50 yards.
Radius of a circle = Diameter of circle / 2
Radius of the circle = 50/2 = 25 yards
Therefore the radius of the circle is 25 yards.
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4y^2 - 37 = 27, what is the positive value of y?
Answer:
y = 4Step-by-step explanation:
[tex]4y^2-37=27\qquad\text{add 37 to both sides}\\\\4y^2=64\qquad\text{divide both sides by 4}\\\\y^2=16\to y=\pm\sqrt{16}\\\\y=-4\ or\ y=4[/tex]
To solve for 'y' in the equation 4y^2 - 37 = 27, you isolate y^2, take the positive square root, and find that the positive value of y is y = 4.
Explanation:To find the positive value of 'y' from the equation 4y^2 - 37 = 27, we first need to isolate y. Starting with 4y^2 - 37 = 27, add 37 to both sides to get 4y^2 = 64. Divide both sides by 4 to isolate y^2, leading to y^2 = 16. Finally, take the square root of both sides. Remember that the square root of a number gives both positive and negative solutions. However, because the question asks for the positive value, we ignore the negative root. Thus, the positive value of y is y = 4.
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The body of a soda can (in between the lid and the bottom) is a cylinder. If the body is about 4.5 inches tall with a diameter of about 2.6 inches, what is the volume of soda the body of the can is able to hold?
Answer: V=7.605π
Step-by-step explanation:
The cylinder formula is V=πr^2h
Substitute the values into the equation.
V=π(1.3)^2(4.5)
V=π(1.69)(4.5)
V=7.605π
Hope this helps!
2. Simplify
(1) 41
5a 2a
(u)
4x-4
*+2x-3
a-5b
2a+b
(iii)
2
5
Answer:
Can you take a pic of the problem if you can't type it out?
Step-by-step explanation:
Answer:
3/10a
Step-by-step explanation:
4/5a - 1/2a
4 × 2a - 1 × 5a/5a × 2a
8a - 5a/10a²
3a/10a²
3/10a
-TheUnknownScientist
The Pick 4 games in many state lotteries announce a four‑digit winning number each day. Each of the 10,000 possible numbers 0000 to 9999 has the same chance of winning. You win if your choice matches the winning digits. Suppose your chosen number is 3079 .
(a) What is the probability that the winning number matches your number exactly?
(Enter your answer rounded to four decimal places.)
=
(b) What is the probability that the winning number has the same digits as your number in any order?
(Enter your answer rounded to four decimal places.)
Answer:
a) P(a)= 0.0001
b) P(b)= 0.0024
Step-by-step explanation:
Given:
Chosen number = 3079
Possible numbers that have chance of winning from 0000 to 9999= 10,000
Winning condition= if made choice matches the winning digits
Now
a)What is the probability that the winning number matches your number exactly?
From 0000 to 9999, only one time can the number 3079 can be the winning number, so
P(a)= 1/10000
= 0.0001
b)What is the probability that the winning number has the same digits as your number in any order?
Winning numbers from 0000 to 10000 that have same digits as 3079 are
4 x 3 x 2 x 1 = 24 ways
Following are the 24 numbers from 0000 to 9999 that have matching digits to 3079:
0379
0397
0973
0937
0793
0739
3079
3097
3970
3907
3790
3709
7039
7093
7930
7903
7390
7309
9073
9037
9370
9307
9730
9703
P(b)= 24/10000
=0.0024 !
Can someone pls help me with this
there is 1 solution of the equation represented on the graph because the line only cuts the graph at one point
Answer:
none
Step-by-step explanation:
The solutions to an equation given graphically are the points where the graph crosses the x- axis.
This graph has no points of intersection with the x- axis and therefore no solutions are shown.
20 POINTS PLZ HELP
Jack is doing an experiment to find the rate of water flow from a tap. He collects the water in a tub and records the height of the water level every five minutes. He then plots the data on a scatter plot. Which equation represents the line of best fit for Jack’s scatter plot?
A. y=14/45x
B. y=45x+15
C. y=45/14x
D. y=14x+45
Answer:
The correct option is C.
Step-by-step explanation:
If a line passing through two point then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the line of best fit passing through the points (0,0) and (14,45). So, the equation of line of best fit is
[tex]y-0=\frac{45-0}{14-0}(x-0)[/tex]
[tex]y=\frac{45}{14}x[/tex]
The equation of line of best fit is [tex]y=\frac{45}{14}x[/tex], therefore the correct option is C.
You sell an automobile part for $9.98, which includes a $.40 sales tax. The article cost you $8.75.
What percentage markup are you charging (to the nearest tenth)?
Answer:
9.5%
Step-by-step explanation:
Buying price of the part= $ 8.75
Selling price of the part= $ 9.98
sale tax= $0.40
Selling price before sale tax= $9.98-$ 0.40 = $ 9.58
Make-up amount charged= $9.58- $8.75 = $ 0.83
As a percentage= (0.83/ 8.75) ×100
=9.5%
Multiply or divide as indicated. x^-8 • x^-2
ANSWER
[tex]\frac{1}{ {x}^{10} }[/tex]
EXPLANATION
The given exponentiial expression is
[tex] {x}^{ - 8} \bullet {x}^{ - 2} [/tex]
We simplify using the rule:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
We apply this property to get:
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = {x}^{ - 8 + - 2}[/tex]
We simplify to get;
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = {x}^{ - 10}[/tex]
We rewrite as a positive index to get;
[tex]{x}^{ - 8} \bullet {x}^{ - 2} = \frac{1}{ {x}^{10} } [/tex]