To win a math game, Lamar has to pick a card with an
expression that has a value greater than 1. The card Lamar chooses
reads (1/2) to the -4 power. Does Lamar win the game? Explain.

:)

120 + 4w is the expression to show the total number of songs on Iris's playlist after w weeks.

She total ahs 120 songs already

She downloads or adds 4 songs every week

An expression to show the total number of songs on Iris's playlist after w weeks is:

120 + 4w

An expression or mathematical expression is a limited combination of symbols that is well-formed according to context-dependent norms. To help identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

Many authors differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical objects.

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Step-by-step explanation:

\( \underline{ \underline{ \text{Given}}} : \)

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)

\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)

⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)

⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)

⤑ \( \sf{ \sqrt{100 - 64}} \)

⤑ \( \sf{ \sqrt{36}} \)

⤑ \( \boxed{ \sf{6\: units}}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)

Hope I helped ! ツ

Have a wonderful day / night ! ♡

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

25°; 115°.

Step-by-step explanation:

all the details are in the attached picture, the answers is marked with red colour.

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer:

6c+7 (c=8)

Step-by-step explanation:

6×8+7

48+7

do the addition answer will come

The value of the expression  6c + 7 at c =8 will be 55.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The value of the expression will be given as:-

E = 6c+7

Put (c=8) in the above expression

E =6×8+7

E = 48+7

E = 55

Therefore the value of the expression  6c + 7 at c =8 will be 55.

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Using a calculator, the value of  csc (203°) is -1.086

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Since csc (203°) = 1/[sin (203°)]

Press 1/ [sin (203°)] and then the equal to button on your calculator. We have:

1/[sin (203°)] = -1.086

Note: If you calculator have "cosec" or "csc" button, you can simply press cosec (203°) or csc (203°) to get the answer.

Thus, the value of  csc (203°) is -1.086

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The probability that a student who attends the first session also attends the second session is 1/3

Evaluating the probability

We can approach this problem by using conditional probability.

Let's use the notation "S1" to represent the event that a student attends the first session, and "S2" to represent the event that a student attends the second session.

Then we can use the formula for conditional probability:

P(S2 | S1) = P(S1 and S2) / P(S1)

We know that P(S1) = 0.6, since 60% of students attend the first session. We also know that P(S1 and S2) = 0.2, since 20% of students attend both sessions.

So we can plug in these values and solve for P(S2 | S1):

P(S2 | S1) = 0.2 / 0.6

P(S2 | S1) = 1/3

Therefore, the probability that a student who attends is 1/3 or approximately 0.333.

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complete question:

In a cooking class 20% of

the students attend two

sessions. 60% of students

attend the first session of

cooking class. What is the

probability that a student that

attends the first session also

attends the second session?

Answer:

a) 0.2218 to 0.7057

b) 0.4710 to 0.8401

Step-by-step explanation:

Given:

sample = n = 18

sample variance = s² = 0.36

To find:

a) 90% confidence interval estimate of the population variance.

b) 90% confidence interval estimate of the population standard deviation.

a)

Compute degree of freedom

degree of freedom = df = n - 1 = 18 - 1 = 17

Compute value of α for a 90% confidence interval  

The confidence level for 90% is:

c = 0.90

So

α = 1 - c = 1 - 0.90 = 0.1

α = 0.1

Now use the table of critical values of the chi-square distribution in order to find critical values. Search for the 17th row of table using df = 17 and find the column corresponding to 1 - α/2 i.e. 0.95 of table for upper tail critical values and column corresponding to α /2 i.e. 0.05 of table for lower tail critical values.

Using the table:

\(X^{2}_{0.95}\) = 8.672

\(X^{2}_{0.05}\) = 27.587

90% Confidence interval estimate of the population variance

The boundaries of CI are computed using formula:

(n−1) s² / \(X^{2}_{\alpha/2}\)  ≤ σ² ≤ (n−1) s² / \(X^{2}_{1-\alpha/2}\)

(n−1) s² / \(X^{2}_{\alpha/2}\)  = (18-1) 0.36 / 27.587

                       = (17) 0.36 / 27.587

                       =  6.12 / 27.587

(n−1) s² / \(X^{2}_{\alpha/2}\)  = 0.2218

(n−1) s² / \(X^{2}_{1-\alpha/2}\) = (18-1) 0.36 / 8.672

                          = (17) 0.36 / 8.672

                          =  6.12 / 8.672

                          = 0.7057

This results in inequalities 0.2218 ≤ σ² ≤ 0.7057 for the variance

b)

90% Confidence interval estimate of the population standard deviation

The boundaries of CI are computed using formula:

√(n−1) s² / \(X^{2}_{\alpha/2}\)  ≤ σ ≤ √(n−1) s² / \(X^{2}_{1-\alpha/2}\)

√(n−1) s² / \(X^{2}_{\alpha/2}\)  = √((18-1) 0.36 / 27.587)

                          = √((17) 0.36 / 27.587)

                          =  √(6.12 / 27.587)

                          = √0.2218

                          = 0.4709

                          = 0.4710

√(n−1) s² / \(X^{2}_{1-\alpha/2}\) = √((18-1) 0.36 / 8.672)

                            = √((17) 0.36 / 8.672)

                            = √ (6.12 / 8.672)

                            = √0.7057

                            = 0.8401

0.4710 ≤ σ ≤ 0.8401 for the standard deviation.

Answer:

Its 9!

Step-by-step explanation:

6×3=18

18/2=9

Hope this helps and don't forget to follow!

Critical points are the points where the slope of the function is zero thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of function g(θ) = sin²(11θ).

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

As per the given function,g(θ) = sin²(11θ).

The critical points are the points where the slope of the tangent of the function is zero.

The slope of the tangent of a function is the first derivative thus,

g'(θ) = 0 ⇒ 2× 11 sin(11θ)cos(11θ) = 0

Sin(11θ) = 0 ⇒ θ = 0

Cos(11θ) = 0 ⇒ 11θ = π/2

θ = π/22

Since, sinusoidal functions are repeating thus,

Next critical point = π/22 + π/22 = π/11 and so on.

Hence "Critical points are the points where the slope of the function is zero thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of function g(θ) = sin²(11θ)".

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The equivalent expressions are B: 2(12m-6p+36) and (c): 12(2m-p+6)

From the question, we have the following parameters that can be used in our computation:

24m-12p+72

Factor out 2 from the expression

So, we have

2(12m-6p+36)

This represents the option (b)

Factor out 12 from the expression

So, we have

12(2m-p+6)

This represents the option (c)

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Part A: The equation could be used to determine p is B0.20+7p = 0.30 + 5p Part B: Two shipping companies is the same for 25 pounds. Company 1 = $7 + (25 - 1) x $0.20 = $11.80 Company 2 = $5 + (25 - 1) x $0.30 = $11.80.

The cost of shipping through two different companies will depend on a variety of factors.

These factors may include the weight and size of the package, the distance it needs to travel, the speed of delivery, and any additional services requested.

Additionally, the cost of shipping may also depend on the type of shipping service used (e.g. ground, air, or express).

To find out the cost of shipping through two different companies, it is best to contact each company directly. This can usually be done by phone, email, or through their website.

Each company will be able to provide a quote based on the package’s specifications. It is then possible to compare the cost of the two shipping companies and determine whether or not the cost is the same.

It is important to note that companies may offer discounts or other incentives for shipping with them.

Therefore, it is important to pay attention to any additional fees or discounts that may apply in order to get the best deal.  

Comparing the cost of two different shipping companies can help to ensure that the most cost-effective option is chosen.

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Answer:

NO

Step-by-step explanation:

No. The sample of only the 2 fastest swimmers on the swim team is not likely to be representative of the entire swim team. It may not include swimmers with different skill levels or performance abilities, which could lead to a biased representation of the team as a whole. To have a representative sample, it would be necessary to include a diverse range of swimmers from different skill levels and performance abilities.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

For every 4 beef cattle there is 3 dairy cattle. For 24 dairy cattle there will be 32 beef cattle as per the given ratio of 3:4.

An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls). The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two things.

Here,

a. No for every 4 beef cattle there is 3 dairy cattle.

b. 4/3=x/24

x=4*24/3

x=32 beef cattle

There are 3 dairy cattle for every 4 beef cattle. According to the stated ratio of 3:4, there will be 32 beef cattle for every 24 dairy cattle.

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The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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Answer:

0.03846154... inches/hour

Step-by-step explanation:

between 10 P.M. and 7:45 A.M. = 9.75 hours

(3/8) inches / 9.75 hours = 0.03846154... inches per hour

EDIT: in fraction form

Answer:

1/26 inches/hour

Step-by-step explanation:

between 10 P.M. and 7:45 A.M. = 9 and 3/4 hours, or 39/4 hours

(3/8) inches / (39/4) hours = 1/26 inches per hour

Answer: 17/5 or 3 2/5

Step-by-step explanation:

You separate the whole numbers from the fractions.

8-5=3 and 4/5-2/5=2/5

Then you combine the fraction with the whole number:

3 2/5 or 17/5 as a mixed fraction.

The composite function of f(x) and g(x) is given as follows:

f(g(x)) = 6x² - 10x - 21.

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The function g(x) in this problem is given as follows:

g(x) = 3x² - 5x - 7.

Hence, for the composite function in this problem, the lone instance of x in f(x) is replaced by 3x² - 5x - 7, as follows:

f(g(x)) = f(3x² - 5x - 7) = 2(3x² - 5x - 7) - 7 = 6x² - 10x - 21.

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The weight of the 0.8-meter piece is 19.6 kilograms.

We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.

Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:

W₁/2.8m = 24.5kg/1m

Solving for W₁, we get:

W₁ = (24.5kg/1m) x 2.8m = 68.6kg

Now we can use the same ratio to find W₂:

W₂/0.8m = 24.5kg/1m

Solving for W₂, we get:

W₂ = (24.5kg/1m) x 0.8m = 19.6kg

Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.

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Answer:

Step-by-step explanation:

Find the area of the outer trapezoid and then subtract the area of the inner trapezoid.

\(A=\frac{1}{2} (a+b)h\)

\(A_o=\frac{1}{2} (6+2)6=24\)

\(A_i=\frac{1}{2} (4+2)3=9\)

Total area = 24 - 9 =15 square units

If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.

A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :

g(x) = {-(1/2)x + 1,    for x<-2

       = {-(x+1)²,        for -2≤x≤1

      =  {4                 for x>1

We have to find the value of g(-5) ,g (-2), and g(-1),

For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,

⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,

For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function

"-(x+1)²" will be used,

⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,

For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,

⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,

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Step-by-step explanation:

to solve this question you need to know that to find the angle you can use the inverse of a trigonometric function. henceforth, we can use arctan for this particular question.

arctan(11/5) is the answer.

the answer correct to 1 decimal point is 65.6 degrees.

comment if you have any doubts.

Answer:

x<0

Step-by-step explanation:

See image below:)

b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

Now, the boat goes Upstream 48 miles, so Downstream must be travelling the same 48 miles back.

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&48&b-c&3\\ Downstream&48&b+c&2 \end{array}\hspace{5em} \begin{cases} 48=(b-c)(3)\\\\ 48=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{48=(b-c)3}\implies \cfrac{48}{3}=b-c\implies 16=b-c\implies \boxed{16+c=b} \\\\\\ \stackrel{\textit{using the 2nd equation}}{48=(b+c)2}\implies \cfrac{48}{2}=b+c\implies 24=b+c\implies \stackrel{\textit{substituting}}{24=(16+c)+c} \\\\\\ 24=16+2c\implies 8=2c\implies \cfrac{8}{4}=c\implies \boxed{2=c}~\hfill~\stackrel{ 16~~ + ~~2 }{\boxed{b=18}}\)

Answer: 1. Perpendicular 2. Bisector 2. Perpendicular Bisector Theorem 3.

Step-by-step explanation:

Answer:

63.45 x 14=888.3

888.3 + 650 = 1,538.3

Step-by-step explanation:

so, if paid in cash right away, it would cost $650.

if financed the TV then costs 14×$63.45 = $888.30

the charge (including interest) to finance the purchase is the difference :

888.30 - 650 = $238.30

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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The area of the triangle will be 108 square inches. Thus, the correct option is D.

Given that:

Height, h = 18 inches

Base, b = 12 inches

Area refers to the measurement of the extent or size of a two-dimensional surface, expressed in square units.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The area of the triangle is given as,

A = 1/2 x 12 x 18

A = 12 x 9

A = 108 square inches

Thus, the correct option is D.

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Step-by-step explanation:

is the answer