The sum of the first 13 terms is 260
How to calculate the sum of the first 13 terms ?The first term(a) is 2
The common difference(d) is 3
n= 13
The formular is
n/2(2a + (n-1)d)
= 13/2 [ 2(2) + (13-1)3]
= 6.5 [4 + 12(3)]
= 6.5 [4 + 36]
= 6.5(40)
= 260
Hence the sum of the first 13 terms is 260
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Cookies are sold in the lunchroom for $2. Ana wants to buy cookies for a group of her friends. If she has $20, write an inequality to show the number of cookies cc she can buy. Use the variable c
As a inequality
Answer:
2c < 20
Step-by-step explanation:
$2 is the price per cookie so 2c is per every cookie, you multiply by 2 to get the price.
Ana only has $20 so the amount of money she spends has to be less then 20 so the inequality would be 2c < 20
Let g(x)=-1/2x+ 6 and h (x) =g(x)-3 which statement descibes the graph of h(x)?
The statement describing the graph of h(x) is "The graph of h(x) is a vertical translation of the graph of g(x) down 3 units".
In the question, are given two graphs g(x) = - (1/2)x + 6, and h(x) = g(x) - 3.
We are asked for the statement that best describes h(x).
Now, h(x) = g(x) - 3, can be seen as the translation of g(x).
For any graph m(x), n(x) is its translation if n(x) = m(x + p) + q.
The translation is vertical is q ≠ 0, and horizontal when p ≠ 0. Also,
if p > 0, then the horizontal translation is p units right,if p < 0, then the horizonal translation is |p| units left,if q > 0, then the vertical translation is q units up, andif q < 0, then the vertical translation is |q| units down.For, h(x) = g(x) - 3, when we compare it with n(x) = m(x + p) + q, we have p = 0, and q = -3.
Since, q ≠ 0, we have vertical translation, and since q < 0, the translation is |q| units down.
Thus, The statement describing the graph of h(x) is "The graph of h(x) is a vertical translation of the graph of g(x) down 3 units".
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The provided question is incomplete. The complete question is:
"Let g(x) = - (1/2)x + 6 and h(x) = g(x) - 3. Which statement describes the graph of h (x)?
The graph of h(x) is a vertical translation of the graph of g(x) up 3 units.The graph of h(x) is a horizontal translation of the graph of g(x) right 3 units.The graph of h(x) is a horizontal translation of the graph of g(x) left 3 units.The graph of h(x) is a vertical translation of the graph of g(x) down 3 units."Wavelength is 0.00004 cm is the weather like for a violet light a large or small value and how do you know
Wavelength is 0.00004 cm is the weather like for a violet light a large or small value and how do you know
The frequency of the violet light is [tex]7.495\times10^{14} s^{-1}[/tex].
Given that,
Wavelength λ=0.00004cm
First, we convert cm to nm
0.00004cm =400nm
These are connected by the equation in electromagnetic radiation (light):
c = λυ
where c refers to the speed of light value is 2.998 x [tex]10^{8}[/tex] m/s, λ refers to wavelength (m) and υ refers to frequency ([tex]s^{-1}[/tex]or Hz).
Now, c = λυ
2.998 x [tex]10^{8}[/tex] m/s=400[tex]\times[/tex][tex]10^{-9}[/tex]m[tex]\times\\[/tex]υ
υ=[tex]\frac{2.998\times10^{8} m/s}{400\times10^{-9}m }[/tex]
υ= [tex]7.495\times10^{14} s^{-1}[/tex]
Therefore, The frequency of the violet light is [tex]7.495\times10^{14} s^{-1}[/tex].
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Each year, Jennifer's school hosts a student vs. teacher basketball tournament to raise money for charity. This year, there are eight teams participating in the tournament. During the first round, each team plays all of the other teams.
(c) Find a numerical method that you could use regardless of the number of the teams in the tournament to calculate the number of games in the first round.
A numerical method that you could use regardless of the number of the teams in the tournament to calculate the number of games in the first round is; (n − 1) + (n − 2) +…+ 1.
What is the Numerical Method used?
The first team will play with the other 7 teams.
Then the second team will play with the 6 other teams, as the game between the first and the second team has already been counted.
Similarly, the third team will play with 5 other teams, and so on. Thus, the
total number of games will be 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28.
Therefore, in the first round there will be 28 games.
If there are 8 teams in the tournament, the number of games in the first round is (8 − 1) + (8 − 2) +…+ 1. Therefore, if there are n teams in the
tournament, the number of games in the first round is given by the sequence; (n − 1) + (n − 2) +…+ 1.
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Which is an equivalent expression for (22 • 34)3?
The equivalent expression of the expression given as: (2^2 • 3^4)^3 is (2^6 • 3^12)
How to determine the equivalent expression?The expression is given as:
(2^2 • 3^4)^3
Expand the exponents of the above expression
(2^2 • 3^4)^3 = (2^2)^3 • (3^4)^3
Evaluate the product of exponents
(2^2 • 3^4)^3 = (2^6) • (3^12)
Rewrite the above expression as:
(2^2 • 3^4)^3 = (2^6 • 3^12)
Hence, the equivalent expression of the expression given as: (2^2 • 3^4)^3 is (2^6 • 3^12)
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Tell me what order these go in
Answer:
I suppose is division multiplication subtraction then addition
Step-by-step explanation:
Explain how you can use a straightedge and a compass to construct an angle that is both congruent.
The construction of two congruent angles using a scale and compass can be done by applying the prerequisite knowledge of construction.
What is an angle?
A geometrical figure formed by using two rays, which are known as the sides of angle. These sides share a common vertex. Angle can be of various types including acute, obtuse, reflex, right, etc.
Explanation of constructing an angle using a scale and compass that is both congruent
Start drawing a line with the scale
Then, using this line or edge of the given angle to construct another corner, with the same vertex, let's call it O
Mark an arc across the sides of the corner using compass
Name the points as A and B, where the arc intersects and extend that arc beyond B
Open the compass to length of AB by setting it to the point B, and then mark an arc that intersects the first arc at point C.
Forthwith, wwe have two congruent components, AB = BC.
As the distance is OA = OB = OC, therefore, ∠AOB and ∠BOC are congruent.
Hence, this is the way of constructing congruent angles using a scale and a compass.
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Rewrite 19/4 as a mixed number. A 9 1/4 B 5 1/4 C 4 3/4 D 4 1/4
Answer:
C) 4 3/4
Step-by-step explanation:
19 divided by 4 doesn't divide equally.
4*5=20 X
4*4=16 YEP
19-16=3
So...
19 can be divided 4 whole times and you're left over with 3.
Thus, it's 4 3/4.
Hope this helps.
Describe the solid that results if the number of sides of each base increases infinitely. The bases of each solid are regular polygons inscribed in a circle.
a. pyramid
The solid that results from increasing the number of sides infinitely is; Close to a Cone
How to describe the nature of a solid object?
We want to describe the solid that results if the number of sides of each base increases infinitely. The bases of each solid are regular polygons inscribed in a circle.
Now, given a pyramid, when its base is a regular polygon whose number of sides increases infinitely, the base gets closer and closer to the shape of a circle, and therefore the solid will be close to a cone.
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. In a triangle, one angle is 5° more than the
measure of the second angle. The third
angle is 10° more than the measure of the
second angle. Find the measure of each
angle angle
The angles are 60°, 55°, and 65°.
Let the triangle be named ΔABC.Let the angle ∠A be "x".Then, the angle ∠B is equal to ∠A + 5°.The angle ∠B is equal to x + 5°.The angle ∠C is equal to ∠A + 10°.The angle ∠C is equal to x + 10°.The angle ∠C is equal to x + 10°.Using the angle sum property of a triangle, we know that the sum of all the angles in a triangle is equal to 180°.∠A + ∠B + ∠C = 180°(x) + (x + 5°) + (x + 10°) = 180°3x + 15° = 180°3x = 165°x = 55°The angle ∠A is equal to 55°.The angle ∠B is equal to 55° + 5° = 60°.The angle ∠C is equal to 55° + 10° = 65°.To learn more about angles, visit :
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b is less than or equal to 6.
options are attached
Answer:
b ≤ 6
This inequality matches the statement, "b is less than or equal to 6."
This is because the sign < tell us that b is going to be less 6, and the line _ tells us that the solution can also be equal to 6.
I need help please I’ll give extra points
Answer:
The answer is A) 1 1/4, I hope it helps
Answer:
x = 5/4
answer is A
Step-by-step explanation:
1 and 4 are supplementary and 2 and 3 are supplementary because they are corresponding angles.
Proved that angle 2 is congruent to angle 4 (∠2 ≅ ∠4).
What are supplementary angles?Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles because the sum of 130° and 50° equals 180°.To proof:
Given:
Angles 1 and 2 are supplementary.Angles 3 and 4 are supplemental.Angle 1 is parallel to angle 3.Show that angle 2 and angle 4 are congruent.This proof includes definitions of congruence and supplementary angles, as well as some equality properties.
∠1 and ∠2 are supplementary (given)∠3 and ∠4 are supplementary (given)∠1 ≅ ∠3 (given)m∠1 + m∠2 = 180°m∠3 + m∠4 = 180° m∠1 + m∠2 = m∠3 + m∠4 (transitive property of equality)m∠1 = m∠3 9congruent angles)m∠1 + m∠2 = m∠1 + m∠4 (substitution property of equality) (replaced m∠3 with m∠1)m∠2 = m∠4 (subtraction property of equality) (subtracted m∠1 from both sides)∠2 ≅ ∠4 (congruent angles)Therefore, the proving is shown.
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The correct question is given below;
Angle 1 and angle 2 are supplementary. Angle 3 and angle 4 are supplementary. Angle 1 is congruent to angle 3. Prove: Angle 2 is congruent to angle 4.
Complete the description of the piecewise function graphed below. Use interval notation to indicate the intervals.
Answers:
[-5, -2]
(-2, 3]
(3, 6]
=====================================================
Explanation:
This piecewise function is made of 3 separate functions of...
f(x) = 5 when [tex]-5 \le \text{x} \le -2[/tex]
f(x) = 4 when [tex]-2 < \text{x} \le 3[/tex]
f(x) = -3 when [tex]3 < \text{x} \le 6[/tex]
--------
The interval [tex]-5 \le \text{x} \le -2[/tex] turns into the interval notation [-5, -2]
Use square brackets to include each endpoint. Each endpoint is included because of the closed filled in points.
In contrast, the interval [tex]-2 < \text{x} \le 3[/tex] has an open hole at -2 and so it turns into (-2, 3]
A similar situation happens with the interval [tex]3 < \text{x} \le 6[/tex] to become (3, 6]
8) the lion at the zoo became ill and lost 6 pounds every week for 3 weeks. in the fourth week, she began to feel better and gained 5 pounds. write and find the value of an expression for the change in the lion's weight.
Answer:
w - 13.
Step-by-step explanation:
Change in weight
= w - 3(6) + 5 where w is her original weight.
= w - 18 + 5
= w - 13.
find a proposition with three variable p, q and r that is true when at most one of the three variables is true, and false otherwise
Three variable p, q and r that is true when at most one of the three variables is true.
How do you identify a proposition?
Propositions are the name for certain types of phrases. A proposition is said to have a "true" truth value if it is true; a "false" truth value if it is untrue. Propositions include statements like "Grass is green" and "2 + 5 = 5". The first claim is true, whereas the second is wrong in terms of truth value.Atmost means maximum.
We have three variables: p,q and r. Maximum one of the three variable is true. However we dont know which variable is true.
Case 1: No variable is true : ¬p ∧¬q∧¬r
Case 2 : p variable is true: p ∧¬q∧¬r
Case 3: q variable is true : ¬p ∧q∧¬r
Case 4 : r variable is true : ¬p ∧¬q∧r
One of the 4 cases has to be true . Thus Case1 or Case 2 or Case3 or Case 4 is true. So we need to take comjuction of the propsitions in each case.
(¬p ∧¬q∧¬r) v (p ∧¬q∧¬r) v (¬p ∧q∧¬r) v (¬p ∧¬q∧r)
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The diorama of a town uses the scale 5 inches : 10 miles. If the diorama measures approximately 60 inches across, what is the approximate measure of town?
Answer: 120 miles
Step-by-step explanation:
We will set up a proportion to solve.
Set up a proportion:
[tex]\displaystyle \frac{5\text{ inches}}{10\text{ miles}} =\frac{60\text{ inches}}{x\text{ miles}}[/tex]
Cross-multiply:
5 * x = 60 * 10
Multiply:
5x = 600
Divide both sides by 5:
x = 120 miles
Find the range of the relation.
A. {-6, -5, -3, -1, 0, 3, 6}
B. {-6, 6}
C. {-6, -3, 0, 3, 6}
D. {-5, -3, -1, 1, 3}
The range of the given relation in the table is option C {-6,-3,0,3,6}
Here first column x represents the domain of the function
Domain is the set of all possible input for the function.
Second column y represents the range of the function
Range is the set of all possible output for the function.
Here the set of all possible inputs of the functions are {-5,-3,-1,1,3}
The set of all possible outcomes of the functions are {-6,-3,0,3,6}
Then the range of the relation in the table = {-6,-3,0,3,6}
Hence, the range of the given relation in the table is option C {-6,-3,0,3,6}
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I REALLY NEED HELP ASAP. Yari says that the product 230×104 has four zeroes. Is she correct? In the box below, explain your answer including how patterns for multiplying by powers of 10 help determine the final answer. Show your work to support your conclusion.
I need help please. I'll mark brainliest.
Yari says that the product 230×10⁴ has four zeroes. She is incorrect.
How to calculate the value?It should be noted that from the information, Yari says that the product 230×10⁴ has four zeroes.
This will be confirmed below:
= 230 × 10⁴
= 230 × 10000
= 2300000
Therefore, the product has 5 zeros. She is incorrect.
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X. Y
-5 -4
-2 -11
1 -18
4 -25
We get the graph for the given points.
We are given the points:
X. Y
- 5 - 4
- 2 - 11
1 - 18
4 - 25
We will plot them on the graph.
In geometry, a coordinate system is a system that makes use of one or extra numbers, or coordinates, to uniquely decide the placement of the factors or different geometric factors on a manifold which include Euclidean space.
In mathematics, the graph of a function f is the set of ordered pairs, where f(x)=y.
A plane is the two-dimensional analogue of a point, a line and three-dimensional space.
Therefore, we get the graph for the given points.
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HELP ME RN PLS IF YK MATH arithmetic operations and function
lol maybe like 8 or something yeah
the standard deviation for using a certain radar speed detector is 0.56 mph for vehicle speeds around 30 mph. if you were traveling 33 mph in a 30 mph zone and if a police officer used this speed detector, what is the probability that you would be clocked at below the speed limit?
0.0001 is a very tiny possibility that you will get caught driving slower than the posted speed limit.
What is probability?Probability is a branch of mathematics that deals with the numerical representations of the likelihood that an event will occur or that a statement is true. A number between 0 and 1 is the probability of that an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
How can you calculate the probability?By simply dividing the actual favorable amount of possibilities by the entire number of possible outcomes, one can use the probability formula to determine the likelihood of an event.
According to the given data:Given,
radar speed detector is 0.56 mph.
inital speed = 33mph
final speed = 30mph
finding the probability that we clocked at below the speed limit.
so,
p(Z<(inital- final)/speed detector)
p(Z<(33-30)/0.56)
p(Z<5.35)
where Z = 1
p(1 - 0.9999)
= 0.0001
0.0001 is a very tiny possibility that you will get caught driving slower than the posted speed limit.
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the water level of a lake fell by 11/2 inches during a 12/3-week long dry spell. Find the average rate at which the water level changed every week.
Every week, the water level dropped by 1.375 inches on average rate.
The average rate is what?
The ratio of "change in the function values" to "change in the interval endpoints" is referred to as the average rate of change of a function f(x) over an interval [a, b]. Specifically, [f(b) - f(a)] can be used to get the average rate of change (b - a). The average rate of change, represented by the symbol A(x), is, in other words, the "ratio of change in outputs to change in inputs." A(x) = (change in outputs), for example (change in inputs)
based on the available facts;
Detailed explanation:
A lake's water level dropped by -11/2 inches throughout the course of a 12-week dry period.
Total fall of water level = -11/2 inches = -5.5 inches
Time of fall = 12/3 week = 4 weeks
Average rate at which water level changed every week=Total fall of water level/Time of fall
=-5.5/4
=-1.375per inch every week
Average rate at which the water level changed every week = -1.375 inches
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Write this number in words: 1.001510512 (with decimals)
The decimal 1.001510512 when written in words is;
One and one million five hundred ten thousand five hundred and twelve hundred millionths
Write the decimal in words?
We can write decimal in words by acknowledging the fact that one part is a whole number while the other part is a fraction. For example;
20.009 in words is; Twenty and nine thousandths
8.406 in words is; Eight and four hundred six thousandths
26.0502 in words is; Twenty-six and five hundred two ten thousandths
6.5904 in words is; Six and five thousand nine hundred four ten thousandths
63.1254 in words is; Sixty-three and one thousand two hundred fifty-four ten thousandths
Thus, we can conclude that the decimal 1.001510512 when written in words is;
One and one million, five hundred ten thousand five hundred and twelve hundred millionths
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X
-5
1
4
6
y
9
0
-7
-1
What is the range of the given function?
{x|x=-5, 1, 4, 6)
y ly=-7, -1, 0, 9}
O {x|x=-7, -5, -1, 0, 1, 4, 6, 9}
O
y ly=-7, -5, -1, 0, 1, 4, 6, 9)
The range of the given function is {y | -7 -1 0 9}
How to determine the range of the given function?The table of values is given as:
x -5 1 4 6
y 9 0 -7 -1
List out the y values
So, we have:
y 9 0 -7 -1
The y values represent the range
So, we have
Range = {y | 9 0 -7 -1}
Order from least to greatest
Range = {y | -7 -1 0 9}
Hence, the range of the given function is {y | -7 -1 0 9}
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how many solutions does the equation 3x-1=3x+1 have
Answer:
0
Step-by-step explanation:
[tex]3x-1=3x+1\\=3x-1-3x=3x+1-3x\\-1=1[/tex]
Due to the fact that the sides are unbalanced, the equation has no true solution.
if a measure is reliable, it: please choose the correct answer from the following choices, and then select the submit answer button. produces a consistent result if the same thing is measured twice. measures what it was intended to measure. predicts actual behavior. co-varies with the independent variable.
A reliable measure is one that (A) produces a consistent result if the same thing is measured twice.
What do we mean by reliable measure?The consistency with which a method attempts to measure something is referred to as its reliability. The measurement is considered reliable if the same result can be consistently obtained by using the same methods under the same conditions. The stability or consistency of test scores is measured by reliability.It can also be defined as the ability of a test or research findings to be repeated. A medical thermometer, for example, is a dependable tool that consistently measures the correct temperature. When the same thing is measured twice, a reliable measure produces the same result.Therefore, a reliable measure is one that (A) produces a consistent result if the same thing is measured twice.
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The correct question is given below:
A reliable measure is one that:
A) produces a consistent result if the same thing is measured twice.
B) measures what it was intended to measure.
C) predicts actual behavior.
D) co-varies with the independent variable.
need help with homework quick!
Answer:
it is the second one(that what I learned in school)
50 POINTS!
Solve for x (and you only have to do odd numbers if you want):
1. 3(x+2)=21
2. 5(2x-1)=-25
3. -4(3x-5)=-16
4. -2(4-x)-5=11
5. 3(-6x+7)+4x=-7
6. 2(3x-4)+5(2x+3)=-9
7. 5(x+9)=65
8. 1/2(x-3)=-4
9. 5x+2(x-6)+7=2
10. 9(x+3)-14x-15=52
1.x=5
2.x=-2
3.x=3
4.x=12
5.x=2
6.x=-1
7.x=4
8.x=-5
9.x=1
10.x=-8
Pls correct me on any of these if I made a mistake
A candy factory makes caramel and chocolate candies. The ratio is two to five. They make 700 pieces of candy a day.
Answer:
They make 200 pieces of caramel candies a day and 500 pieces of chocolate candies a day.
Step-by-step explanation:
Since the ratio is two to five, make it 2x + 5x = 700.
7x = 700
x=100
So, for caramel candies, 2 x 100 = 200
For chocolate candies, 5 x 100 = 500