what am i doing wrong? i cannot figure out why i can't get the surface area. the answer says it's 69.3cm^3. please help me

The inverse property of logarithms states that log base b of x is equal to y if and only if b raised to the power of y is equal to x.

The correct equations that use the inverse property of logarithms are:

   8^7 = 87, so log8(87) = 7.

   7^7 = 7, so 8log7(7) = 7.

   7^8 = 8, so 7log7(8) = 8.

   8^7 = 78, so log8(78) = 7.

Therefore, the correct answers are:

   log8(87) = 7

   8log7(7) = 7

   7log7(8) = 8

   log8(78) = 7

Hence, the options (a), (b), (d), and (f) are correct.

The equations that correctly use the inverse property of logarithms are: log8(87) = 7, 8log8(7) = 7, and 8log7(8) = 7.

The inverse property of logarithms states that if log base a of b equals c, then a raised to the power of c equals b. In the given options, the equations that satisfy this property are:

log8(87) = 7: This equation can be rewritten as 8^7 = 87, which holds true

8log8(7) = 7: This equation can be simplified as 7 = 7, which is true.

8log7(8) = 7: This equation can be rewritten as 7^7 = 8, which is correct.

The other equations, 8log7(7) = 7, log8(78) = 7, and 7log7(8) = 8, do not satisfy the inverse property of logarithms as they do not yield the original values of the bases when raised to the powers indicated by the logarithms.

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Answer:

48⁰

Step-by-step explanation:

TAKE NOTE: The sum of interior angles of a triangle equals 180.

STEP 1: SET UP YOUR EQUATION

x + 50 + 82 = 180

STEP 2: SOLVE

x + 50 + 82 = 180

x + 132 = 180

x = 48

Every member of the family of functions y = ae^(r1x) + be^(r2x) is also a solution of the differential equation 7y" + 34y' - 5y = 0.

Let's find the values of r so that the function y = ex satisfies the differential equation 7y" + 34y' - 5y = 0.

To find the values of r, we substitute the function into the differential equation.

7y" + 34y' - 5y

= 0 becomes

\(7e^x + 34e^x - 5e^x\)

= 0

Simplifying gives us:

36e^x = 0e^x = 0

We see that e^x can never be zero, so there are no values of r for which y = ex satisfies the given differential equation.

The two values we obtained from part (a) are r1 = 5/7 and r2 = 0. To show that every member of the family of functions y = ae^(r1x) + be^(r2x) is a solution of the differential equation 7y" + 34y' - 5y = 0, we need to substitute the function into the differential equation and check if it satisfies the equation.

Let y = ae^(r1x) + be^(r2x)7y" + 34y' - 5y = 0 becomes:

\(7(a*r1*r1*e^(r1x) + b*r2*r2*e^(r2x)) + 34(a*r1*e^(r1x) + b*r2*e^(r2x)) - 5(a*e^(r1x) + b*e^(r2x)) = 0\)

Expanding and simplifying gives us:

\(ae^(r1x)(7r1*r1 + 34r1 - 5) + be^(r2x)(7r2*r2 + 34r2 - 5) = 0\)

Since r1 and r2 satisfy the differential equation 7y" + 34y' - 5y = 0, we have:7r1*r1 + 34r1 - 5 = 0 and 7r2*r2 + 34r2 - 5 = 0

Therefore, every member of the family of functions y = ae^(r1x) + be^(r2x) is also a solution of the differential equation 7y" + 34y' - 5y = 0.

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Answer: Obtuse

Would appreciate brainly <3

Given a well-balanced algebraic expression, we can construct a corresponding expression syntax tree using the postfix notation. This involves converting the infix expression to postfix and then building an evaluation tree.

To construct an expression syntax tree, we first need to convert the given infix expression to postfix notation. We can achieve this by using the infixToPostfix algorithm, which uses a stack to convert the infix expression to postfix notation. For example, the infix expression 4 + ((7 + 9) * 2) would be converted to postfix notation as 479+2*+.

Next, we can use the postfix expression to build an evaluation tree. This is done by starting at the first element of the postfix expression and moving left to right. When an operator is encountered, we pop the top two nodes from the stack, create a new node with the operator as its value and the two popped nodes as its left and right children, and push the new node onto the stack.

Once the evaluation tree is constructed, we can perform an infix traversal of the tree to obtain the infix expression. This involves traversing the tree in an inorder fashion (left subtree, current node, right subtree) and appending the nodes' values to form the infix expression. In our example, the infix traversal of the evaluation tree would give us

\((4 + ((7 + 9 )* 2 )).\)

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In   linear equation, 2 hours and 45 minutes, the temperature of the pork roast is 165 ° F.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The temperature of the pork roast is greater at 3 hours than at 2 hours and 45 minutes.

After 2 hours and 45 minutes, the temperature of the pork roast is 165 ° F.

    f(a) = 67  the temperature of the pork roast is 67° F. When it is placed in the over .

     f( 2.45 ) = the temperature  of pork roast is 65° F when its done cooking.

 f( 2.45 ) = the temperature  of pork roast decrease between 2 hours and                        

                          45 min and 3 hours .

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The t-statistic is 0 based on regression equation.

To compute the missing value, we need to use the regression equation: y = mx + b. We know that the adjusted r squared is 0.4, so the coefficient of determination is 0.4. This means that 40% of the variation in y can be explained by the variation in x.

We also know that the mean residual sum of squares is 9.6, which is the average of the squared differences between the predicted values and the actual values.

Using these values, we can find the regression equation:

y = mx + b
0.4 =\(slope of regression^2 * variance of x / variance of y\)

Since the variance of x is 1.67 and the variance of y is unknown, we can solve for the slope of regression:

slope of regression = \(\sqrt{(0.4 * variance of y / 1.67) }\)

Next, we can use the slope of regression to find the missing value:

y = mx + b
0 = slope of regression * 0 + b
b = 0

Therefore, the regression equation is:

y = slope of regression * x

Using the remaining data points, we can find the slope of regression:

(0,0) -> (1,0): slope = 0 / 1 = 0
(1,0) -> (2,0): slope = 0 / 1 = 0
(2,0) -> (3,-?): slope = (-?) / 1 = -slope of regression

Since we know that the slope of regression is -2, we can solve for the missing value:

(-?) / 1 = 2
-? = 2
? = -2

Therefore, the missing value is -2.

To find the t-statistic used to test the null hypothesis that the slope of regression is equal to -2, we need to use the following formula:

t = (slope of regression - hypothesized slope of regression) / standard error of slope

The standard error of slope is given by:

SE = \(\sqrt{(mean residual sum of squares / (n - 2) / variance of x) }\)

Using the values given in the problem:

SE = \(\sqrt{(9.6 / (3 - 2) / 1.67)}  = \sqrt{(9.6 / 1.67)}\) = 2.57

Therefore, the t-statistic is:

t = (-2 - (-2)) / 2.57 = 0

The t-statistic is 0.

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Answer:

False.

Step-by-step explanation:

The statement "1:24,000" is not an example of a verbal statement. It is a numerical ratio or scale commonly used in cartography and map scales. Verbal statements typically involve spoken or written language rather than numerical representations. :)

Answer:

Step-by-step explanation:

(√x + √3)(√x + 2√3) = (√x)² + 3√3√x + 2(√3)² = x + 3√(3x) + 6

Answer:

144ft

Step-by-step explanation:

Length x Wifth x height

We have: P(brown then yellow) = 2/11 and P(green then green) = 2/132.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

let's calculate the probability of selecting a brown marble followed by a yellow marble without replacement:

P(brown then yellow) = (4/12) * (6/11) = 24/132 = 2/11

We multiply 4/12 (the probability of selecting a brown marble on the first draw) by 6/11 (the probability of selecting a yellow marble on the second draw, after one brown marble has already been removed). Note that we divide by 11 on the second draw, as there are now only 11 marbles left in the bag.

Now let's calculate the probability of selecting two green marbles without replacement:

P(green then green) = (2/12) * (1/11) = 2/132

We multiply 2/12 (the probability of selecting a green marble on the first draw) by 1/11 (the probability of selecting another green marble on the second draw, after one green marble has already been removed). Again, note that we divide by 11 on the second draw, as there are now only 11 marbles left in the bag.

So, we have:

P(brown then yellow) = 2/11

P(green then green) = 2/132

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Two crucial tasks inherent in the initial stage of group therapy are orientation and establishing group norms.Ambiguity and lack of a structured approach in groups often lead to confusion, inefficiency, and potential challenges.

Orientation involves providing essential information to group members about the purpose, goals, and guidelines of the therapy group.

It helps individuals understand what to expect, builds trust, and creates a sense of safety and predictability within the group. Orientation may include discussing confidentiality, group rules, expectations, and addressing any questions or concerns.

Establishing group norms involves collaboratively developing shared guidelines and expectations that govern the behavior and interactions within the group. This process allows group members to contribute to the creation of a supportive and respectful group climate. Group norms help set boundaries, encourage open communication, and foster a sense of cohesion among members.

Without clear structure and guidance, group members may struggle to understand their roles, goals, or the process of the group therapy. Ambiguity can hinder progress, create frustration, and impede meaningful communication.

Lack of structure may also result in difficulty managing conflicts, decision-making, or time management within the group. It can lead to unequal participation, power struggles, and a lack of accountability.

To address these issues, it is important for group therapy to provide a clear framework, establish ground rules, and facilitate structured activities or interventions that promote clarity, engagement, and progress. A structured approach helps create a supportive environment, enhances group dynamics, and maximizes the therapeutic benefits of the group process.

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Answer:

(7, 8)

Step-by-step explanation:

We know

Point A is located at (5,8) and is translated two units to the right.

Translate to the right mean the x will increase; in this case, it translated two units to the right meaning the x will increase b 2.

So, the coordinate of A will be at (7, 8)

Answer:

x = 1

Y = 1

Step-by-step explanation:

A. 3(2x-3y= - 1)

6x-9y=- 3

B. -2(3x-4y= - 1)

- 6x+8y=2

Add both equations:

(6x-9y= - 3) + (- 6x+8y=2)

-y= - 1

3x - 4(1) = - 1

3x-4= - 1

3x = 4 - 1

= 3/3 = 1

The expression

f(t) = 5t + 11

Is read verbally as, "function of t at 5t plus 11."

This is alredy

Hello

5/8 of 6

= 5/8 x 6

= 30/8

= 3,75

1hour = 60min

5min => 3,75

60min => ?

? = 60 x 3,75 ÷ 5 = 45

Lan drinks 45 ounce glasses in 1 hour.

The value of euros can be converted to dollars by simply multiplying euro by 1.06 so 120 euros be 127.89 dollars.

Unit conversion is the process of converting the dimension of a given quantum between colorful units, frequently by multiplicative conversion factors that alter the value of the measured volume without altering its goods.

The sanctioned currency of 20 of the EU's 27 member countries is the euro( symbol€; law EUR)( EU). By of 2023, this group of countries — officially known as the eurozone or euro area — will have around 344 million residers. One euro is equal to one hundred cents.

The United States bone ( symbol$; law USD; frequently shortened asUS$ orU.S. Bone to separate it from other bone - nominated currencies; also known as the bone ,U.S. bone , American bone , or informally buck) is the sanctioned coin of the United States and multitudinous other nations.

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=πr^2h

=π(5)^2*11

=25*11π

=275π yd^3

Answer:

2770.9 in³

Step-by-step explanation:

A cylinder has a base radius of 7in and a height of 18in. What is its volume in cubic inch to the nearest tenths place?

The formula for the volume of a cylinder is given as:

πr²h

r = radius = 7 in

h = height = 18 in

Hence:

Volume of the cylinder = π × 7² × 18

= 2770.88472 in³

Approximately to the nearest tenth = 2770.9 in³

Answer:

6795.2 in

Step-by-step explanation:

This is the Correct Answer Like it and Put a Heart.

The coordinates of the point on the unit circle corresponding to a central angle of 21 degrees are (0.93, 0.36), which is answer choice c.

The point on the unit circle corresponding to a central angle of 21 degrees can be found using the trigonometric functions sine and cosine.

In this case, the x-coordinate is equal to the cosine of the angle and the y-coordinate is equal to the sine of the angle.

Converting degrees to radians, we have:

x = cos(21) = 0.93

y = sin(21) = 0.36

A unit circle in mathematics is a circle with a radius of one, or one unit. The unit circle is frequently the circle with radius 1 that is located at the origin (0, 0) in the Cartesian coordinate system on the Euclidean plane, notably in trigonometry.

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Answer:

X =20

X+24=2(x+22)

X+24=2x+44

X=44-24

X=20

Answer:

What are the answers?

Step-by-step explanation:

The amount of money Jimmy spends on video games is directly proportional to the number of games he owns.

If A is directly proportional to B, it means A and B will change at the same rate and at the same direction. If A is made twice greater then B will be twice greater as well.

If the relation between A and B can be expressed as a linear equation:

A = kB + C

where k is a constant, then A is directly proportional to B.

Let:

x = the money Jimmy spends on video games

y = the number of games Jimmy owns

From the problem, we can conclude:

x = 50 (y - 333)  

since he will only pay after the 333th video game.

Re-arrange the equation:

x = 50y - 16,650

Notice that the above equation is a linear equation, hence x is directly proportional to y.

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A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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Answer:

5)  DE = 7 units and DF = 4 units

6)  ST = 8 units

\(\textsf{7)} \quad \sf OM=\dfrac{3}{2}\:units\)

8)  x ≤ -3 and x ≥ 3

Step-by-step explanation:

Information from Parts 1-4:

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Points A and D are the points of intersection of the two functions.  

To find the x-values of the points of intersection, equate the two functions and solve for x:

\(\implies g(x)=f(x)\)

\(\implies x^2-9=-x+3\)

\(\implies x^2+x-12=0\)

\(\implies x^2+4x-3x-12=0\)

\(\implies x(x+4)-3(x+4)=0\)

\(\implies (x-3)(x+4)=0\)

Apply the zero-product property:

\(\implies (x-3)= \implies x=3\)

\(\implies (x+4)=0 \implies x=-4\)

From inspection of the graph, we can see that the x-value of point D is negative, therefore the x-value of point D is x = -4.

To find the y-value of point D, substitute the found value of x into one of the functions:

\(\implies f(-4)=-(-4)=7\)

Therefore, D = (-4, 7).

The length of DE is the difference between the y-value of D and the x-axis:

⇒ DE = 7 units

The length of DF is the difference between the x-value of D and the x-axis:

⇒ DF = 4 units

To find point S, substitute the x-value of point T into function g(x):

\(\implies g(4)=(4)^2-9=7\)

Therefore, S = (4, 7).

The length ST is the difference between the y-values of points S and T:

\(\implies ST=y_S-y_T=7-(-1)=8\)

Therefore, ST = 8 units.

The given length of QR (⁴⁵/₄) is the difference between the functions at the same value of x.  To find the x-value of points Q and R (and therefore the x-value of point M), subtract g(x) from f(x) and equate to QR, then solve for x:

\(\implies f(x)-g(x)=QR\)

\(\implies -x+3-(x^2-9)=\dfrac{45}{4}\)

\(\implies -x+3-x^2+9=\dfrac{45}{4}\)

\(\implies -x^2-x+\dfrac{3}{4}=0\)

\(\implies -4\left(-x^2-x+\dfrac{3}{4}\right)=-4(0)\)

\(\implies 4x^2+4x-3=0\)

\(\implies 4x^2+6x-2x-3=0\)

\(\implies 2x(2x+3)-1(2x+3)=0\)

\(\implies (2x-1)(2x+3)=0\)

Apply the zero-product property:

\(\implies (2x-1)=0 \implies x=\dfrac{1}{2}\)

\(\implies (2x+3)=0 \implies x=-\dfrac{3}{2}\)

As the x-value of points M, Q and P is negative, x = -³/₂.

Length OM is the difference between the x-values of points M and the origin O:

\(\implies x_O-x_m=o-(-\frac{3}{2})=\dfrac{3}{2}\)

Therefore, OM = ³/₂ units.

The values of x for which g(x) ≥ 0 are the values of x when the parabola is above the x-axis.

Therefore, g(x) ≥ 0 when x ≤ -3 and x ≥ 3.

Answer:

.242 Kilograms

Step-by-step explanation:

To convert milligrams to kilograms multiply the value by .000001 or move the decimal mark 6 places to the left.

Answer:

0.242 kg

Step-by-step explanation:

divide the mass by 1e+6

Answer:

x(x-2)=168

x=14

Step-by-step explanation:

Let the length of the rectangle be x.

width=(x-2)

x(x-2)=168

x^2-2x=168

x=14, x=-12 (rejected)