Gigi earned $65 for 5 hours of gardening. She earned $90 for 9 hours of office work. Which statement correctly compares Gigi’s earning per hour for gardening and office work?
a. She earned $3 more per hour for office work than for gardening.
b. She earned $4 more per hour for office work than for gardening.
c. She earned $3 more per hour for gardening than for office work.
d. She earned $4 more per hour for gardening than for office work.

This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, the exact decimal or simplified fraction solution is \(\frac{7}{20}\).

To solve the expression \(\frac{79}{40}\) - 162.5%, we first need to convert the percentage to a decimal.
To convert a percentage to a decimal, we divide it by 100.

So, 162.5% becomes \(\frac{162.5}{100}\) = 1.625.
Now, we can rewrite the expression as \(\frac{79}{40}\) - 1.625.
To subtract fractions, we need a common denominator.

In this case, the least common multiple (LCM) of 40 and 1 is 40.

So, we need to rewrite both fractions with the denominator of 40.
For the first fraction, \(\frac{79}{40}\), we can multiply both the numerator and denominator by 1 to keep it the same.
For the second fraction, 1.625, we can multiply both the numerator and denominator by 40 to get \(\frac{65}{40}\)
Now we can subtract the fractions:

\(\frac{79}{40} - \frac{65}{40} = \frac{79-65}{40}\)

= \(\frac{14}{40}\)
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\(\frac{79}{40} - 162.5\%\) is equal to \(\frac{7}{20}\) or \(0.35\) as a decimal. To solve the expression \(\frac{79}{40}-162.5\%\), we have to follow some step.

Steps to solve the expression:

1. Convert the percentage to a decimal: \(162.5\% = \frac{162.5}{100} = 1.625\)

2. Now, we have \(\frac{79}{40}-1.625\).

3. In order to subtract fractions, we need a common denominator. The least common denominator (LCD) for 40 and 1 is 40.

4. Rewrite the fractions with the common denominator:

    \(\frac{79}{40}-1.625 =\frac{79}{40}- (1.625 * \frac{40}{40})\)

                     \(= \frac{79}{40}  - \frac{65}{40}\)

5. Subtract the fractions:

    \(\frac{79}{40} - \frac{65}{40} = \frac{79-65}{40}\)
                    \(= \frac{14}{40} \)

6. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2 in this case:

    \( \frac{14}{40} = \frac{(\frac{14}{2})}{(\frac{40}{2})}\)

        \(= \frac{7}{20}\)

Therefore, the simplified answer to \(\frac{79}{40}-162.5\%\) is \(\frac{7}{20}\) or \(0.35\) as a decimal.

In conclusion, \(\frac{79}{40}-162.5\%\) is equal to \(\frac{7}{20}\) or \(0.35\) as a decimal.

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Answer:

A

Step-by-step explanation:

Got this right on edmentum

At least 68% of the data falls between 62 and 78, and at least 95% of the data falls between 54 and 86.

To answer this question, we can use the empirical rule, also known as the 68-95-99.7 rule, which tells us that for a normal distribution:

Using this rule, we can estimate the fraction of the data that falls between the following pairs:

Between 54 and 86:

To find the range of values that is within two standard deviations of the mean, we can subtract and add two standard deviations from the mean:

Lower bound: 70 - 2*8 = 54

Upper bound: 70 + 2*8 = 86

So, about 95% of the data falls between 54 and 86.

Between 62 and 78:

To find the range of values that is within one standard deviation of the mean, we can subtract and add one standard deviation from the mean:

Lower bound: 70 - 8 = 62

Upper bound: 70 + 8 = 78

So, about 68% of the data falls between 62 and 78.

Therefore, we can conclude that at least 68% of the data falls between 62 and 78, and at least 95% of the data falls between 54 and 86.

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Answer:

i believe the answer is 4r - 3b

Answer:

4r+3b

Step-by-step explanation:

4 red awarded = 4r

3 blue awarded = 3b

Score = 4r + 3b

The value of y.\($$P_3(0.5)=6(0.5)^3+\frac{5-8y}{2}(0.5)^2+\frac{23-8y}{2}(0.5)=\frac{3}{4}y+\frac{17}{4}$$$$\Rightarrow \frac{3}{4}y+\frac{17}{4}=0.75b+1.5c+3$$$$\Rightarrow \frac{3}{4}y+\frac{17}{4}=0.75(\frac{5-8y}{2})+1.5(\frac{23-8y}{2})+3$$$$\Rightarrow y=-\frac{3}{4}$$\)Hence, the value of y is -3/4.

Given that P3(x) is the interpolating polynomial for the data points (0,0), (0.5,y), (1,3) and (2,2).

We need to find the y value if the coefficient of \(x3 in P3(x)\)is 6.Interpolation is the process of constructing a function from given discrete data points. We use the interpolation technique when we have a set of data points, and we want to establish a relationship between them.To solve the given problem, we need to find the value of the polynomial P3(x) for the given data points. The general expression for a polynomial of degree 3 can be written as:

\($$P_3(x)=ax^3+bx^2+cx+d$$\)

To find P3(x), we can use the method of Lagrange Interpolation, which is given by:

\($$P_3(x)=\sum_{i=0}^3y_iL_i(x)$$\)

where

\($L_i(x)$\)is the Lagrange polynomial. We have three data points, so we get three Lagrange polynomials\(:$$\begin{aligned} L_0(x)&=\frac{(x-0.5)(x-1)(x-2)}{(0-0.5)(0-1)(0-2)} \\ L_1(x)&=\frac{(x-0)(x-1)(x-2)}{(0.5-0)(0.5-1)(0.5-2)} \\ L_2(x)&=\frac{(x-0)(x-0.5)(x-2)}{(1-0)(1-0.5)(1-2)} \\ L_3(x)&=\frac{(x-0)(x-0.5)(x-1)}{(2-0)(2-0.5)(2-1)} \\ \end{aligned}$$\)Now, we can substitute these values in the equation of $P_3(x)$:\($$P_3(x)=y_0L_0(x)+y_1L_1(x)+y_2L_2(x)+y_3L_3(x)$$We know that the coefficient of x3 in P3(x\)) is 6. Therefore, the equation of P3(x) becomes:\($$P_3(x)=6x^3+bx^2+cx+d$$\)

Now we substitute the given values in the equation of $P_3(x)$ to get the value of y. The given data points are (0, 0), (0.5, y), (1, 3), and (2, 2).When we substitute (0, 0) in $P_3(x)$, we get:\($$P_3(0)=6(0)^3+b(0)^2+c(0)+d=0$$\)Hence, d=0.When we substitute (0.5, y) in $P_3(x)$, we get:\($$P_3(0.5)=6(0.5)^3+b(0.5)^2+c(0.5)=0.75b+1.5c+3=y$$$$\Rightarrow 0.75b+1.5c=-3+y$$\)When we substitute (1, 3) in $P_3(x)$, we get:\($$P_3(1)=6(1)^3+b(1)^2+c(1)=6+b+c=3$$$$\Rightarrow b+c=-3$$\)When we substitute (2, 2) in $P_3(x)$, we get:\($$P_3(2)=6(2)^3+b(2)^2+c(2)=48+4b+2c=2$$$$\\)Rightarrow 4b+2c=-23$$We can solve the above three equations simultaneously to get the values of b and c.$$b+c=-3\ldots(1)\($$$$0.75b+1.5c=-3+y\ldots(2)$$$$4b+2c=-23\ldots(3)$$\)Multiplying equation (1) by 0.5, we get:$$0.5b+0.5c=-1.5\ldots(4)$$Subtracting equation (4) from equation (2), we get:$$0.25b+0.5c=y-1.5\($$$$\Rightarrow 2b+4c=4y-12\ldots(5)$$\)Substituting equation (1) in equation (5), we get:\($$2b-6=4y-12\Rightarrow 2b=4y-6$$\)Substituting this value in equation (3), we get:$$8y-24+2c=-23\Rightarrow c=\frac{23-8y}{2}$$Substituting this value of c in equation (1), we get:$$b+\frac{23-8y}{2}=-3\($$$$\Rightarrow b=\frac{5-8y}{2}$$\)Now, we substitute the values of b and c in $P_3(x)$:\($$P_3(x)=6x^3+\frac{5-8y}{2}x^2+\frac{23-8y}{2}x$$\)The coefficient of x3 in P3(x) is 6.

Hence,\($$6=\frac{6}{2}\Rightarrow a=1$$$$\Rightarrow P_3(x)=6x^3+\frac{5-8y}{2}x^2+\frac{23-8y}{2}x$$\)We can now substitute x=0.5 in $P_3(x)$ and get the value of y.\($$P_3(0.5)=6(0.5)^3+\frac{5-8y}{2}(0.5)^2+\frac{23-8y}{2}(0.5)=\frac{3}{4}y+\frac{17}{4}$$$$\Rightarrow \frac{3}{4}y+\frac{17}{4}=0.75b+1.5c+3$$$$\Rightarrow \frac{3}{4}y+\frac{17}{4}=0.75(\frac{5-8y}{2})+1.5(\frac{23-8y}{2})+3$$$$\Rightarrow y=-\frac{3}{4}$$\)Hence, the value of y is -3/4. Answer:  The value of y is -3/4.

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To find the distance traveled by the car in the time interval from t = 0 to t = 9 seconds, we need to integrate the velocity function over that interval.

The velocity function is given by \(\(v(t) = 3t \sqrt{81 - t^2}\).\)

To find the distance traveled, we integrate the absolute value of the velocity function over the interval [0, 9]:

\(\[\text{{Distance}} = \int_{{0}}^{{9}} |v(t)| \, dt\]\)

Since the velocity function \(\(v(t)\)\) is non-negative over the interval [0, 9], we can simply integrate the velocity function from 0 to 9:

\(\[\text{{Distance}} = \int_{{0}}^{{9}} v(t) \, dt\]\)

Let's calculate the distance traveled:

\(\[\text{{Distance}} = \int_{{0}}^{{9}} 3t \sqrt{81 - t^2} \, dt\]\)

We can simplify this integral using a substitution. Let's substitute \(\(u = 81 - t^2\) and \(du = -2t \, dt\). When \(t = 0\), \(u = 81\), and when \(t = 9\), \(u = 0\)\). The integral becomes:

\(\[\text{{Distance}} = \int_{{81}}^{{0}} -\frac{3}{2} \sqrt{u} \, du\]\)

Now we can evaluate the integral:

\(\[\text{{Distance}} = -\frac{3}{2} \int_{{81}}^{{0}} \sqrt{u} \, du\]\)

We can reverse the limits of integration and change the sign:

\(\[\text{{Distance}} = \frac{3}{2} \int_{{0}}^{{81}} \sqrt{u} \, du\]\)

Integrating \(\(\sqrt{u}\) with respect to \(u\)\) gives us:

\(\[\text{{Distance}} = \frac{3}{2} \left[ \frac{2}{3} u^{3/2} \right]_{{0}}^{{81}}\]\)

Evaluating the integral at the limits:

\(\[\text{{Distance}} = \frac{3}{2} \left[ \frac{2}{3} (81)^{3/2} - \frac{2}{3} (0)^{3/2} \right]\]\)

Simplifying:

\(\[\text{{Distance}} = \frac{3}{2} \left( \frac{2}{3} \cdot 81^{3/2} - 0 \right)\]\)

\(\[\text{{Distance}} = 3 \cdot 81^{3/2}\]\)

Evaluating the expression:

\(\[\text{{Distance}} = 3 \cdot 9^3 = 3 \cdot 729 = 2187 \text{{ ft}}\]\)

Therefore, the distance traveled by the car in the 9 seconds from t = 0 to t = 9 is 2187 ft.

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The probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.

To analyze the given scenario and calculate the probabilities for all six possible scenarios, let's create a decision tree and timeline to visualize the information provided.

Timeline:

Year 1: Initial investment of $12 million in new technology.

Year 2: Results evaluated by shareholders.

Year 3: Final decision made by shareholders.

Decision Tree:

```                 ┌─── Continue (95%)

                │

       15% ─────┼─── Continue (75%)

                │

$12 million ─────┼─── Continue (40%)

investment       │

                │

       10% ─────┼─── Abandon ($5 million cost)

                │

                │

        5% ─────┼─── Abandon ($5 million cost)

                │

                └─── Abandon ($5 million cost)

```

Now, let's calculate the probabilities for each scenario:

1. New equipment reduces expenses by 15% (40% probability):

  Probability = 40% * 95% = 0.4 * 0.95 = 0.38 (38%)

  Outcome: The shareholders vote to continue for another 3 years.

2. New equipment reduces expenses by 10% (30% probability):

  Probability = 30% * 75% = 0.3 * 0.75 = 0.225 (22.5%)

  Outcome: The shareholders vote to continue for another 3 years.

3. New equipment reduces expenses by 5% (30% probability):

  Probability = 30% * 40% = 0.3 * 0.4 = 0.12 (12%)

  Outcome: The shareholders vote to continue for another 3 years.

4. New equipment does not reduce expenses (10% probability):

  Probability = 10%

  Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.

5. New equipment reduces expenses by 15%, but shareholders vote to abandon (5% probability):

  Probability = 15% * (1 - 95%) = 0.15 * 0.05 = 0.0075 (0.75%)

  Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.

6. New equipment reduces expenses by 10%, but shareholders vote to abandon (5% probability):

  Probability = 10% * (1 - 75%) = 0.1 * 0.25 = 0.025 (2.5%)

  Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.

To summarize, we have calculated the probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.

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The equation of the translated function is:

g(x) = (x + 3)^2 - 2

We can see that the blue graph is a translation of the red one, where the equation for the red graph is:

f(x) = x^2

Remember that the translations are:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.

If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

By analyzing the vertices, we can see that the vertex of the blue graph is at (-3, -2) so we have a translation of 3 units to the left and 2 units down, meaning that we have:

g(x) = f(x + 3) - 2 = (x + 3)^2 - 2

So the correct option is A.

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According to the given statement the probability of the surgery being successful on exactly two patients is 0.441 & 44.1%.

To find the probability of the surgery being successful on exactly two patients, we can use the binomial probability formula.
The formula for the probability of exactly k successes in n trials, when the probability of success in a single trial is p, is given by:
P(X = k) = nCk × \(p^{k}\) × \((1-p)^{n-k}\)
In this case,

n (number of trials) is 3 (since the surgery is performed on three patients),

p (probability of success) is 0.7 (given that the surgery has a 70% chance of success),

and

k (number of successes) is 2 (since we want exactly two successful surgeries).
Plugging the values into the formula, we have:
P(X = 2) = 3C2 × 0.7² × (1-0.7)³⁻²

Simplifying the calculation:

P(X = 2) = 3 × 0.7² × 0.3¹
Calculating the result:
P(X = 2) = 0.441
Therefore, the probability of the surgery being successful on exactly two patients is 0.441, or 44.1%.

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The probability of the surgery being successful on exactly two out of three patients is 0.441 or 44.1%.

The probability of the surgery being successful on exactly two patients can be found using the binomial probability formula.

The formula for the probability of exactly x successes in n trials, when the probability of success in each trial is p, is given by:

\(P(x) = (n_C_x) * p^x * (1-p)^{n-x}\)

In this case, the probability of success (the surgery being successful) is 0.7, as stated in the question.

Since the surgery is performed on three patients (n = 3), we want to find the probability of exactly two successful surgeries (x = 2).

Plugging these values into the formula, we get:

\(P(2) = (3_C_2) * 0.7^2 * (1-0.7)^{(3-2)}\)

Calculating the values, we find:

\(P(2) = 3 * 0.7^2 * 0.3^1\)

\(P(2) = 3 * 0.49 * 0.3\)

\(P(2) = 0.441\)

Therefore, the probability of the surgery being successful on exactly two patients is 0.441 or 44.1%.

In conclusion, the probability of the surgery being successful on exactly two out of three patients is 0.441 or 44.1%.

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The initial population will double in about 27.73 years.

The population will reach β*K after about 25.44 years.

What is logistic regression?

The logistic model in statistics is a statistical model that depicts the likelihood that an event will occur by making the event's log-odds a linear combination of one or more independent variables. In regression analysis, logistic regression is used to estimate a logistic model's parameters.

The logistic equation is given by:

dy/dt = ry(1 - y/K)

(a) If y0=K/3, we want to find the time t at which the initial population has doubled.

Let Y denote the population size, so we want to find the value of t such that Y(t) = 2*K.

To solve for t, we need to first solve the differential equation using separation of variables:

dy/[y(1 - y/K)] = r*dt

Integrating both sides, we get:

ln|y/K - 1| - ln|y| = r*t + C

where C is a constant of integration. Solving for y, we get:

y(t) =\(K / [1 + Ae^{(-rt)}]\)

where A is a constant determined by the initial condition y(0) = K/3. Substituting this initial condition, we get:

K/3 = K / [1 + A]

Solving for A, we get:

A = 2

Substituting this value of A, we get:

y(t) = \(K / [1 + 2e^'(-rt)}]\)

Now, we need to find the time t such that Y(τ) = 2*K. Substituting Y(t) = y(t)*K, we get:

Y(t) =\(K^2 / [1 + 2e^{(-rt)}]\)

So we need to solve the equation:

2K = \(K^2 / [1 + 2e^{(-rt)}]\)

Solving for t, we get:

t = (1/r) * ln(2)

Substituting r = 0.025 per year, we get:

t = (1/0.025) * ln(2) ≈ 27.73 years

Therefore, the initial population will double in about 27.73 years.

(b) If y0/K=α, we want to find the time T at which y(T)/K=β. Letting Y denote the population size, we want to find the value of T such that Y(T) = β*K.

Following a similar procedure as in part (a), we can solve the logistic equation and obtain:

y(t) = \(K * [α/(α + (1 - α)*e^{(-rt)})]\)

Substituting Y(t) = y(t)*K, we get:

Y(t) = K *\([α/(α + (1 - α)e^{(-rt)})] = \beta K\)

Solving for t, we get:

t = (1/r) * ln[(β/α) - 1] - (1/r) * ln[(1 - α)/α]

Substituting r = 0.025 per year, α = 0.1, and β = 0.9, we get:

t = (1/0.025) * ln[8] - (1/0.025) * ln[9] ≈ 25.44 years

Therefore, the population will reach β*K after about 25.44 years.

The initial population will double in about 27.73 years.

The population will reach β*K after about 25.44 years.

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Measure of angle:

∠A  = 36.86°

∠B = 90°

∠C = 53.13 °

Measure of side ,

AB =  28

BC = 21

CA = 35

Given triangle ABC.

Right angled at B.

Now, using trigonometric ratios to find angle A , B , C .

Right angled at B : ∠B = 90°

Angle A,

SinA = 21/35

∠A = 36.86

Angle C,

SinC = 28/35

∠C = 53.13

Now measures of side.

To find the length of side use sine rule .

Sine rule:

a/sinA = b/sinB = c /sinC

a = opposite side of angle A .

b = opposite site of angle B .

c = opposite side of angle C.

AB = 28

BC = 21

CA = 35

Hence the sides and angles of the triangles are measured .

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Answer:

24

Step-by-step explanation:

36 Divided by three times 2 = 24 since fractions are division problems

Answer:

24 pots have daisies in them.

Step-by-step explanation:

36÷3= 12 and 12×2=24

Answer:

4/9ths of a cup of sugar is needed for one cup of flour.

Step-by-step explanation:

To answer this you need to scale the number of cups of flour up from 3/4 to 1  that ratio would be 4/3 (multiplying a fraction by its own reciprocal will give you 1).

We can then simply take that ratio, and scale the sugar by the same amount:

1/3 * 4/3 = 4/9

Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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The more plausible explanation for the association between diet soda consumption and weight gain is that people who drink diet soda may have other factors or behaviors that contribute to weight gain.

For example, individuals who drink more diet soda may have a higher intake of calorie-dense foods or may engage in less physical activity.

Additionally, people who are already overweight or at risk of gaining weight.

May be more likely to choose diet soda as a way to manage their weight.

While the large sample size may provide strong statistical evidence of the association between diet soda consumption and weight gain.

It does not necessarily prove a causal relationship.

Further research is needed to establish a cause-and-effect relationship between diet soda consumption and weight gain.

Such as randomized controlled trials or longitudinal studies.

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Answer:

12.56 sq units

Step-by-step explanation:

C= 2 times pi times radius

12.56=2(3.14)R

12.56=6.28

r=2

area=A = πr²

A = 3.14(2²) = 3.14(4) = 12.56

Answer:

n+7

Step-by-step explanation:

Sum means add, so it's just n added to 7:

n+7 :)

Answer:

n+7 is the answer or u can put it in parenthesis (n+7)

Step-by-step explanation:

Answer:

formula for ratio: you can write a ratio with :, or, /

x axis is horizontal

0= x axis  6= y axis

Step-by-step explanation:

Answer:

x² + 18xi - 81

Step-by-step explanation:

FOIL - First, Outside, Inside, Last

Step 1: Write out expression

(x + 9i)²

Step 2: Expand

(x + 9i)(x + 9i)

Step 3: FOIL

F - x²

O - 9xi

I - 9xi

L - 81i²

Step 4: Combine

x² + 18xi + 81i²

Step 5: Simplify

i² = -1

x² + 18xi + 81(-1)

x² + 18xi - 81

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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The null hypothesis for the single factor ANOVA states that all means are equally true.

The null hypothesis for a single-factor ANOVA (analysis of variance) states that all means are equal.

The alternative hypothesis, on the other hand, suggests that at least one of the means is different from the others.

The purpose of the ANOVA test is to determine whether there is sufficient evidence to reject the null hypothesis and conclude that there are significant differences between the means. A statistical formula used to compare variances across the means (or average) of different groups.

Hence, the statement is true .

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Answer:

either b or c

Step-by-step explanation:

i think

The last column evaluates to "T" in all rows. Therefore, the argument is valid since the conclusion always follows from the premises.

Let's assign symbols to represent the statements in the argument:

P: The boss snaps at you.

Q: You make a mistake.

R: The boss is irritable.

The argument can be symbolically represented as follows:

[(P ∧ Q) → R] ∧ ¬P → ¬R

To determine the validity of the argument, we can construct a truth table:

P | Q | R | (P ∧ Q) → R | ¬P | ¬R | [(P ∧ Q) → R] ∧ ¬P → ¬R

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

T | T | T |      T      |  F |  F |          T          |

T | T | F |      F      |  F |  T |          T          |

T | F | T |      T      |  F |  F |          T          |

T | F | F |      F      |  F |  T |          T          |

F | T | T |      T      |  T |  F |          F          |

F | T | F |      T      |  T |  T |          T          |

F | F | T |      T      |  T |  F |          F          |

F | F | F |      T      |  T |  T |          T          |

The last column represents the evaluation of the entire argument. If it is always true (T), the argument is valid; otherwise, it is invalid.

Looking at the truth table, we can see that the last column evaluates to "T" in all rows. Therefore, the argument is valid since the conclusion always follows from the premises.

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Answer:

$2 was the dollar gain for the stock XYZ

Answer:

Inverse of f exists.

Step-by-step explanation:

From the graph attached,

If we do the horizontal line test for the function graphed,

We find the function as one to one function.

In other words for every input value (x-value) there is a different output value.

Since, for one-to-one functions, inverse of the functions exist.

Therefore, the answer will be,

The inverse of 'f' exists.

Answer:

\(D.\ 4\frac{1}{2}\)

Step-by-step explanation:

Remember : 1 1/2 = (2+1)/2 = 3/2

Formula :

\(\large \text Volume\ V \ of \ a \ rectangular \ prism \ =base\ \times\ height\)

Then

\(V=\left( 2\times 1\frac{1}{2} \right) \times 1\frac{1}{2}\)

   \(=\left( 2\times \frac{3}{2} \right) \times \frac{3}{2}\)

   \(=3 \times \frac{3}{2}\)

   \(=\frac{9}{2}\)

   \(=\frac{8+1}{2} = \frac{8}{2} +\frac{1}{2} =4+\frac{1}{2} =4\frac{1}{2}\)

The percentage of bags of cookies that will contain between 64 and 68 cookies is approximately 18.23%.The number of cookies in a shipment of bags is normally distributed, with a mean of 64 and a standard deviation of 4.

What percentage of bags of cookies will contain between 64 and 68 cookies

When X is normally distributed with mean µ and standard deviation σ, the z-score formula can be used to find the probability that X is between two values.

Z = (X - µ) / σ

First, we convert both 64 and 68 to z-scores:

Z for 64 cookies = (64 - 64) / 4 = 0Z for 68 cookies = (68 - 64) / 4 = 1

Next, we find the probability that X is between these two z-scores using a standard normal distribution table or calculator:

Prob (0 < Z < 1) = 0.3413 - 0.5(0) - 0.159

= 0.1823

So, the percentage of bags of cookies that will contain between 64 and 68 cookies is approximately 18.23%.

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