What is the measure of this angle?

60
80
120
125

Answer:

-------------------------------

We observe that the sequence is decreasing with common difference of - 3.

Therefore, this is an AP, with the first term of t(1) = 13 and common difference of d = -3.

Use the nth term formula for AP:

Answer:

a)  Arithmetic sequence

b)  t(n) = 16 - 3n

Step-by-step explanation:

An Arithmetic Sequence has a constant difference between each consecutive term.

A Geometric Sequence has a constant ratio (multiplier) between each consecutive term.

From inspection of the given table, t(n) decreases by 3 each time n increases by 1.  Therefore, the sequence is arithmetic with a common difference of -3.

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given:

Substitute the initial value (when n = 1) and the common difference into the formula to create an equation for the nth term:

[tex]\implies t(n)=13+(n-1)(-3)[/tex]

[tex]\implies t(n)=13-3n+3[/tex]

[tex]\implies t(n)=16-3n[/tex]

By using the recursive formula for the sequence, we will see that the second term is:

f(2) = -4

We know that the sequence is defined by the recursive formula:

f(1) = 3

f(n + 1) = -3*f(n) + 2

(notice that the formula is written incorrectly in the question, as it not completely defines a sequence).

We want to find the second term of the sequence, which is f(2).

Using the second part of the formula, we will get:

f(2) = -3*f(1) + 2

And we know that f(1) = 3

Then:

f(2)= -3*3 + 2

f(2) = -6 + 2 = -4

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The values of trigonometric functions are sinα = -10 and cotα =  -10/24.

What is the trigonometric functions?

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[) are real functions that relate an angle of a right-angled triangle to ratios of two side lengths.

They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.

We have given,

tanα = -(24/10)  and π α < 2π

To Find: sinα =? & cotα = ?

 [tex]{\displaystyle \tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}}\tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}[/tex]

cotα =   -10/24

sinα = -10

Therefore, the values of trigonometric functions are sinα = -10 and  cotα =   -10/24.

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The length of given point is 1 units. The total length of the actual path followed by an object is called as distance.

Use the formula d = st, or distance equals speed times time, to find the distance. Since both represent a certain amount of distance per unit of time, such as miles per hour or kilometres per hour, rate and speed are comparable. If speed s and rate r are equal, then r = s = d/t.

Here,

Given :

Distance Formula

=> [tex]\sqrt{(x_{2}- x_{1} )^{2} + (y_{2}- y_{1} )^{2} }[/tex]

=> [tex]\sqrt{6- 5 )^{2} + (0 )^{2} }[/tex]

=> 1

Therefore , The length of given point is 1 units. The total length of the actual path followed by an object is called as distance.

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The function is  A = 120[tex](1.016)^{4t}[/tex] and the balance after 6 years is  $175.64.

What is compound interest?

The interest that is calculated using both the principal and the  interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Here the principal = $120

Rate of interest = 6.4%  = 6.4/100 = 0.064C. Then,

Now using compound interest formula then,

Amount A = P[tex](1+\frac{r}{n} )^{nt}[/tex]

Here n=4 compound quarterly

A = 120[tex](1+\frac{0.064}{4} )^{4t}[/tex]

=> A= 120[tex](1+0.016)^{4t}[/tex]

=> A = 120[tex](1.016)^{4t}[/tex]

The function is A = 120[tex](1.016)^{4t}[/tex]. Now years t = 6 then

=> A = A = 120[tex](1.016)^{4*6}[/tex] = 120[tex](1.016)^{24}[/tex]

=> A =  $175.64

Hence the function is  A = 120[tex](1.016)^{4t}[/tex] and the balance after 6 years is  $175.64 .

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Answer:

The pharmacy has 8 pints of cough syrup and a prescription calls for 3/4 of a pint, so to find the number of full prescriptions that can be filled, you would divide 8 (the total amount of cough syrup) by 3/4 (the amount of cough syrup per prescription). This would be 8 / (3/4) = 8 * (4/3) = 8 * 1.33 = 10.67.

Therefore, they can fill 10 prescriptions, they will have 0.67 left.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

lets bring the numbers down here.

7,7,2,4,6,7,8,8,8,8,9,0,0,4,4

By arranging them from least to greatest.

0 ,0 ,2 ,4, 4, 4, 6, 7 ,7, 7 ,8 ,8 ,8 ,8 ,9

the median(middle number) is 7

We see that the y-intercept of the line is 4 while slope = -3/2.

The slope indicates the steepness of a line and the intercept indicates the location where it intersects an axis. The slope and the intercept define the linear relationship between two variables, and can be used to estimate an average rate of change.

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = − 7 x + 4 , we see that the y-intercept of the line is 4.

slope = (-2 - 1) / (4 - 2) = -3 / 2

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Answer: m∠ABC = 54° and m∠​DBC= 30°

Step-by-step explanation: To find the measures of each angle, you have to make it into an equation to solve for .

In this case, the equation is (3x + 3) + (6x - 1) = 83°

First you combine like terms. In this case the 3x and the 6x have to be combined. 3x + 6x = 9x. The 3 and -1 have to be combined as well. 3 - 1 = 2.

Now you have 9x + 2 = 83°

Subtract 2 from each side and you are left with 9x = 81°.

Now divide each side by 9 and you are left with x = 9.

Now that you know the value of x, you will have to apply it to the equation for each angle.

m∠ABC = 6(9) - 9 = 53

m∠ABC = 53°

m∠​DBC = 3(9) + 3 = 30

m∠​DBC = 30°

In conclusion, the measure of angle ABC 53° and the measure of angle DBC is 3°.

Hoped this helped!!

Answer:

m∠ABC = 54° and m∠​DBC= 30°

The algebraic expression that she can use to represent the scenario would be = $x-25/2

Algebraic expression is defined as the expression that can be used to represent a constant algebraic number, variables, and the algebraic operations.

The amount of money Tamika and her friend sold their old toys= X dollars

The amount of money that Tamika had to pay back to her parents = $25

Therefore the remaining amount = X - 25

The amount of money that she divided between her friend and her = $ x-25/2

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Answer:

last

Step-by-step explanation:

last because isometry is a shape moving rotating or reflecting across but sides are same since square became bigger and rhombus thinner only triangle is left

The expressions that are sums or differences of two cube:

A. 64 + a¹²b⁵¹

B. –t⁶ + u³v²¹

C. 8h⁴⁵ – k¹⁵

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

The following phrases are sums or differences of two cubes:

A. 64 + a¹²b⁵¹

=4³+(a⁴b¹⁷)³

B. –t⁶ + u³v²¹

=(-t²)³+(uv⁷)³

C. 8h⁴⁵ – k¹⁵

=(2h¹⁵)³-(k⁵)³

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If the correlation between 2 variables is 1.00, the standard error of estimate equals 0 statement is True.

The statistical measure of correlation, which is expressed as a number, describes the magnitude and direction of a relationship between two or more variables. A correlation between two variables does not, however, automatically mean that a change in one variable was what led to changes in the values of the other.

The two events are causally related, which means that causation demonstrates that one event is the result of the occurrence of the other event. It is also known as the cause-and-effect principle.

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Answer:

30%

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} & \sf Jazz&\sf Blues & \sf Ragtime & \sf Total\\\cline{1-5} \sf Adult & 14& 15&11 & 40\\\cline{1-5} \sf Children &36 &6& 18& 60\\\cline{1-5} \sf Total &50 &21 &29 & 100\\\cline{1-5}\end{array}[/tex]

From observation of the table:

To find the percent of the children surveyed that preferred ragtime music, divide the number of children that preferred ragtime music by the total number of children:

[tex]\begin{aligned}\implies \sf Percent&=\dfrac{\sf Children\;who\;preferred\;ragtime}{\sf Total\;children}\\\\&=\dfrac{18}{60}\\\\&=\dfrac{18 \div6}{60\div 6}\\\\&=\dfrac{3}{10}\\\\&=\dfrac{3 \times 10}{10 \times 10}\\\\&=\dfrac{30}{100}\\\\&=30\%\end{aligned}[/tex]

4 ounces ate 328 calories : 1312 calories.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

The given 4 ounces ate 328 calories

and 1 pound = 16 ounces

16/4= 4

4 * 328 = 1312

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the interest Bianca will collect is $3127.50.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

where P is the principal amount of money, R is the interest rate as a decimal, T is the time.

p = 3000

r =4.25%

t =1

S = 3000*4.25*1/100 = 127.50

Hence the interest Bianca will collect is $3127.50.

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The probabilities are 5/36 and 9/36, respectively, if the sum is bigger than 6 and if the amount is divisible by 5 or 6 (or both).

Probability theory is the study of how likely it is that an event will occur or that a statement is true. A number between 0 and 1, roughly 0 signifying how unlikely an event is to occur and 1, signifying certainty, is the probability of an event occurring. The likelihood or likelihood that a particular event will occur is expressed numerically as a probability. It is also possible to express probabilities as percentages between 0% and 100% or as percentages between 0 and 1. the percentage of all possible outcomes divided by the total number of events in a complete collection of equally likely alternatives that result in a specific occurrence.

given

It may take the following forms:

(4,6),(5,5),(5,6),(6,5),(6,6)

the likelihood that the total exceeds 9 is 1/36+1/36+1/36+1/36.

=5/36.

B) The following are some possible scenarios:

(1,4),(4,1),(3,3),(3,2),(4,2),(5,1),(1,5),(6,4),(4,6)

The likelihood that the number will be divisible by five, six, or both is

1/36 plus eight times

=9/36

Therefore, The probabilities are 5/36 and 9/36, respectively, if the sum is bigger than 6 and if the amount is divisible by 5 or 6 (or both).

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On solving the provided question, we can say that if the length of GF IS 8 unit then  the length of HI(Diameter) = 16 unit.

The diameter of a circle cuts through the center whereas the radius extends from the center to the edges of the circle. The diameter of a circle effectively divides the shape in two.

A chord is a straight line that is drawn between two points on a circle when it is used in mathematics (or more generally, on any curve). A table of chords was the first trigonometric table ever discovered. Nowadays, the sine is employed in its place (sines and chords are connected), but chords might be more understandable to some people.

Radius is "GF"

diameter is "HI"

Cord is "EJ".

If the length of GF IS 8 unit

then the length of HI(Diameter) = 16 unit.

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The total area under the density curve for X must be exactly 1.

The region below the density curve and above the values of X that make up the event is the likelihood of any event. There must be exactly one area under the density curve for all instances of X.

A Density Curve: What Is It?

The general shape of a distribution is depicted by a density curve. The percentage of all observations falling in a certain period is represented by the area under the curve and above any interval of values on the horizontal axis. A density curve's median is the location where the area to the left and right are equal.

A graph that displays probability is known as a density curve. All probabilities are represented by 100% of the curve's area under the curve. You can alternatively state that the area is equal to 1 because 100% is a decimal, which is how we typically express probabilities.

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Answer: t/w

Step-by-step explanation: It's the reciprocal, so you have to flip both. 9/5 = w/t,   5/9 = t/w

Answer:

y=2/5x+6

Step-by-step explanation:

work attached here

No, Her goal was to earn $300 but she managed to earn only $270, selling calendars.

Any system that divides time into discrete units, such as days, months, or years, and places those units in a specific order is known as a calendar. A calendar is useful for keeping track of historical events, religious holidays, and other observances, as well as for scientific and historical research.

The word is derived from calendae (or kalendae), the first day of the month in the Roman republican calendar, the day on which future market days, feasts, and other occasions were announced. Calendae is the Latin word for "interest register" or "account book," which is itself a derivation from calendae.

Given that:

Cost of each calendar = $9

Number of calendar sold to the family = 16

Number of calendar sold to the neighbourhood = 14

So, The total number of calendar sold by Celia = The number of calendar sold to the family + The number of calendar sold to the neighbourhood

Total number of calendar sold by Celia = 16 + 14 = 30

The cost of each calendar = $ 9

The cost of 30 calendar = $ 9 × 30 = $ 270

Therefore, she could not reach her goal as her goal was to earn $300 but she managed to earn only $270.

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Answer:

0.10 and 0.90 are the correct answers.

Step-by-step explanation:

The length of GC could be 7.2 when Triangle GHC is similar to triangle JKC.

What is a triangle ?

Triangle can be defined in which it contains 3 sides and 3 angles and the sum of three angles is 180 degrees .

Given

Triangle GHC is similar to triangle JKC

JK = 15

KC = 20

JC = 18

GH = 6

SO,

△GHC ~ △JKC

we know that

(GH/GC) = (JK/JC)

(6/GC) = (15/18)

GC= 6 * 18 / 15

GC = 36 / 5

GC = 7.2

Hence , the length of GC could be 7.2 when Triangle GHC is similar to triangle JKC.

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Answer:

60

Step-by-step explanation:

2(7)^2 -5(7) -3

2(49) -35 -3

98 -35 -3

63 -3

60

Answer:

he earns $500 from the lessons from both groups of students.

Step-by-step explanation:

To summarize:

There are 14 students in set R (piano students)

There are 10 students in set R (piano students) who are not in set S (saxophone students)

There are 11 students in set S (saxophone students)

There are 14 + 11 = 25 total students in both sets R and S

There are 4 students who are common to both R and S, that are taking saxophone for free

The music teacher will get $280 for the piano students

The music teacher will get $220 for the saxophone students.

So the total he earns is $280 + $220 = $500 from the lessons from both groups of students.

There are only three correct equations for the area of the right triangle which are:

The area of a triangle is calculated by dividing the product of the base and height of the triangle.

base of the triangle = x

height of the triangle = x + 2

area of the triangle = 1/2(x)(x + 2)

so

1/2(x)(x + 2) = 24...(1)

1/2 is also 0.5, so the equation 0.5(x)(x + 2) = 24 is correct.

by cross multiplication, equation (1) becomes;

x(x + 2) = 48

x² + 2x = 48 {expand the left hand side}

x² + 2x - 48 = 0 {subtract 48 from both sides}

so the equation x² + 2x - 48 = 0 is correct.

Considering the last equation, x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x = 100 - 4 {collect like terms}

2x² + 4x = 96 {divide through by 2}

x² + 2x = 48

x² + 2x - 48 = 0

so the equation x² + (x + 2)² = 100 is equivalent to the equation (1) and so is also correct.

Therefore, the equations 0.5(x)(x + 2) = 24, x² + 2x - 48 = 0, and x² + (x + 2)² = 100 are correct and can be used to find the length of sides for the right triangle.

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Jana's rode her bike 12 miles in 45 minutes, so Jana's rate per hour is 16 miles/hour.

Given that, Jana is training for a triathlon that includes a 112 mile bike ride.

What is the speed?

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Today she rode her bike 12 miles in 45 minutes.

Here, 45 minutes =45/60 =3/4

Speed =Distance/Time

= 12 ÷ 3/4

= 12 × 4/3

= 16 miles/hour

Therefore, Jana's rode her bike 12 miles in 45 minutes, so Jana's rate per hour is 16 miles/hour.