A radioactive substance has an initial mass of 475 grams and a half-life of 20 days. What equation is used to determine the number of days, x, required for the substance to decay to 63 grams?



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Sampling methods that may be biased for finding the percentage of defective boards in a sawmill production are: selecting 30 consecutive boards, emailing customers and relying on their responses, and selecting every 40th board produced. So, the correct answer is A, B and D.

The biased sampling methods are Examining 30 consecutive boards one hour after production begins may be biased because it only captures a snapshot of the production at that specific time, and the boards selected may not be representative of the entire batch produced during the day.

Emailing customers to ask about defective boards may be biased because the response rate may vary among customers, and customers who experienced a higher or lower number of defective boards may be more likely to respond.

Selecting 20 boards at random each day for 5 days and examining them is less likely to be biased, as long as the selection process is truly random and representative of the entire production.

Selecting every 40th board produced over the course of one week is also less likely to be biased if the production process is consistent and there are no patterns or variations in the production that would affect the quality of every 40th board. So, the correct answer for biased is A, B and D.

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Answer:

• f(x) is stretched away from the x-axis by a factor of 2 and is reflected over the x-axis.

Step-by-step explanation:

The function f(x) = 2sin(2x) has an amplitude of 2 and a period of π/2. When we apply the rule g(w) = - f(x), we are reflecting the graph of f(x) over the x-axis and then taking its opposite. This means that the amplitude of g(w) will still be 2, but the graph will be reflected and stretched away from the x-axis by a factor of 2.

I hope it helps you

Answer:

3

Step-by-step explanation:

Because same numbers = same y intercept but I'm not sure

Answer:

  1) The image has the same slope, different y-intercept

Step-by-step explanation:

You want the relationship between the line 3x -5y = 4 and its image dilated by a factor of 5/3 centered at the origin.

Dilation about the origin multiplies every coordinate by the dilation factor. Dilation does not change slopes or angles, but it changes lengths by the dilation factor.

When the equation of a line is written in standard form, the dilation of it effectively multiplies the constant by the dilation factor.

The given line has intercepts ...

  ax +by = c

  x-intercept = c/a = 4/3

  y-intercept = c/b = -4/5

If these values are multiplied by the dilation factor 5/3, they become ...

  x-intercept' = (5/3)(4/3) = 20/9 = 2 2/9

  y-intercept' = (5/3)(-4/5) = -4/3 . . . . . note the y-intercept has changed

The slope of the given line can be determined from its intercepts:

  m = (-y intercept)/(x intercept) = -(-4/5)/(4/3) = 3/5

Since both of these intercepts are multiplied by the same dilation factor, their ratio remains unchanged. The slope of the dilated line is the same.

Effectively, the dilated line's equation is ...

  3x -5y = 4(5/3)

  3x -5y = 20/3

__

Additional comment

The original (dashed) line and its dilated image are shown in the attachment.

Answer:6

Step-by-step explanation:

The Inequality which ensure triangle exists is 22 > 4x > 7.

Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."

Theorem used In ΔABC,

AB + BC >AC

AC+ BC >AB

AC + AB > BC

According to the question,

In triangle ABC.

AC = 18units

BC = 6x units,

AB = 2x + 4 units

.

Substitute the value in the inequality to ensure triangle exists we get 4x > 7 and 22 > 4x.

From (1) and (2) inequality of triangle we get 22 > 4x > 7.

Hence, Inequality which ensure triangle exists is 22 > 4x > 7.

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Which inequality represents the values of that ensure triangle exists? a triangle with these side lengths: AC = 18 units, BC = 6x units, and AB = 2x + 4 units

The length of the third side ​of a triangle cannot be 15 cm

The correct answer is an option (b)

We know that the triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

For example if a, b, c represents the side of a triangle then by above theorem a + b ≥ c

Here, the two sides of a triangle measure 4 cm and 8 cm.

Let a = 4 cm and b = 8 cm and c represents the third side of a triangle.

Using triangle inequality theorem,

a + b ≥ c

4 + 8 ≥ c

12 ≥ c

This means that the third side of the triangle must be less than or equal to 12 cm.

Thus, the correct answer is an option (b)

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The complete question is:

A triangle has two sides measuring 4 cm and 8 cm. Which lengths cannot be the length of the third side ​

a) 7 cm

b) 15 cm

c) 10 cm

d) 5 cm

Answer: x=4

Step-by-step explanation:

Isolate x using opposite operations.

2x + 3 = 11

2x = 8

x = 4

Answer:

4

Step-by-step explanation:

subract 3 from 11

2x=8

divide by 2

x=4

The height of the cylinder, given the volume and the diameter of the base, would be 2, 592.46 feet

The given diameter of the base is 10 inches, so we need to find the radius first. The radius is half the diameter:

Radius (r) = Diameter / 2 = 10 inches / 2 = 5 inches

We also need to convert the radius from inches to feet since the volume is given in cubic feet:

5 inches = 5/12 feet = 0.4167 feet

Volume of a cylinder:

Volume (V) = πr²h

450π = π x (0.4167)^2 x h

450 = (0.4167)^2 x h

h = 450 / (0.4167)^2 = 2, 592.46 feet

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Answer:

1Step-by-step explanation:

The equation of the line parallel to PQ that passes through the point (6, -1) is y = (-5/6)x + 4.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that: the coordinates of P are (-3, 8) and the coordinates of Q are (9, -2).

We can find the slope of line PQ.

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of points P and Q, respectively.

m = (-2 - 8) / (9 - (-3))

m = -10 / 12

m = -5/6

Since we want the equation of a line parallel to PQ, it will have the same slope.

Hence, the equation of the line can be written as:

y - y1 = m(x - x1)

where (x1, y1) is the point (6, -1) and m is the slope we found earlier.

Plugging in the values, we get:

y - (-1) = (-5/6)(x - 6)

y + 1 = (-5/6)x + 5

y = (-5/6)x + 5 - 1

y = (-5/6)x + 4

Therefore, the equation of the parallel line to PQ is y = (-5/6)x + 4.

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The number of feet per second that the remote control car travels is: 5 ft/s

The formula to find the speed from distance and time is:

Speed = Distance/time

Now, we are given:

Time: t = 3/40 seconds

Distance = 3/8 ft

Thus:

Speed = (3/8)/(3/40)

Speed = (3/8) * (40/3)

Speed = 5 ft/s

Thus, that is the speed that the remote control car travels

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We would need 168 square inches of Teflon to completely cover the triangular prism machinery.

To calculate the surface area of a triangular prism, we need to find the area of each face and then add them up. Let's assume that the triangular bases of the prism have base b and height h, and that the length of the prism is l.

The surface area of the triangular bases is (1/2)bh for each base, so the total area is (1/2)bh + (1/2)bh = bh.

The lateral surface area of the prism is the area of the three rectangular faces. Each rectangular face has length l and height h, so the total lateral surface area is 3lh.

Therefore, the total surface area of the triangular prism is

bh + 3lh

To determine how much Teflon is needed to cover the machinery, we need to know the dimensions of the triangular prism. Once we have those dimensions, we can calculate the surface area using the formula above and then use that value to determine the amount of Teflon required.

Let's say the base of the triangular prism is 4 inches and the height is 6 inches, and the length of the prism is 8 inches. Then the surface area of the triangular prism is

bh + 3lh

= (4 in. x 6 in.) + 3(8 in. x 6 in.)

= 24 in² + 144 in²

= 168 in²

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The only congruence theorem that cannot be used to prove these triangles to be congruent is option B, AAS (Angle-Angle-Side).

The SAS (Side-Angle-Side), SSS (Side-Side-Side), and ASA (Angle-Side-Angle) congruence theorems all involve matching corresponding sides and angles of two triangles. However, AAS only matches two angles and a non-included side, which is not enough to guarantee congruence in all cases.

In fact, the AAS congruence theorem only works if the given non-included side is between the two given angles, forming a "triangle sandwich" with the two given angles as the bread and the non-included side as the filling.

If the non-included side is not between the two given angles, then it is possible to have two non-congruent triangles with the same angle measures, but different side lengths.

Therefore, the AAS congruence theorem cannot be used to prove all cases of triangle congruence, making it the only option that cannot be used to prove these triangles to be congruent

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False. While all relationships should be valued and respected, it's unrealistic to say that they all have equal weight. Some relationships may be closer and more intimate than others, or may require more time and energy to maintain.

Additionally, some relationships may have greater consequences or impact on our lives than others. It's important to prioritize and nurture our relationships based on their individual significance and value to us.
In the context of relationships, the term "weight" refers to the importance or influence of a particular relationship. Not all relationships have equal weight because the significance of each relationship varies based on factors such as trust, communication, shared experiences, and emotional connections.

Some relationships are naturally stronger and more influential than others due to these factors, making them more valuable and impactful in a person's life. In contrast, weaker relationships may not have the same level of trust, connection, or influence, making them less important overall. It is essential to recognize and nurture the stronger relationships in one's life to maintain a healthy support system and overall well-being.

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Answer:9

Step-by-step explanation:

Answer:

75lbs

Step-by-step explanation:

if the mean of the packages was 15 then all the items averaged to 5 pounds each meaning they had a total of 15*5 or 75lbs

Step 1: The test statistic is 56.56.

Step 2: Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.

Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.

Step 4: The test statistic of 56.56 is greater than the critical value of 18.307.

Step 5:  The 90% confidence interval for the variance of force on the helmets is [1615.46, 4123.82]

In statistics, variance is a measure of the spread or dispersion of a set of data points. It is calculated as the average of the squared differences from the mean.

Step 1: To test whether the standard deviation is significantly less than 40, we can use a chi-square test with the null hypothesis H0: [tex]σ^{2}[/tex] ≥ 1600 lbs² and the alternative hypothesis H1: σ² < 1600 lb[tex]s^{2}[/tex]. The test statistic is:

chi-square = (n - 1) *[tex]s^{2}[/tex] / [tex]σ^{2}[/tex]

where n is the sample size, [tex]s^{2}[/tex] is the sample variance, and [tex]σ^{2}[/tex] is the population variance under the null hypothesis.

Substituting the given values, we have:

chi-square = (31 - 1) * 2350 / 1600 = 56.56

Rounding to two decimal places, the test statistic is 56.56.

Step 2: To determine the p-value for a left-tailed test, we need to find the area under the chi-square distribution to the left of the test statistic. Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.

Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.

Step 4: Since the test statistic of 56.56 is greater than the critical value of 18.307, we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the standard deviation is significantly less than 40 at the 5% level of significance.

Step 5: To calculate a 90% confidence interval for the variance of force on the helmets, we can use the formula:

[(n - 1) * [tex]s^{2}[/tex]/ chi-square upper, (n - 1) * [tex]s^{2}[/tex] / chi-square lower]

where chi-square upper and chi-square lower are the upper and lower critical values, respectively, from the chi-square distribution table for 30 degrees of freedom at the 5% level of significance. Substituting the given values, we have:

chi-square upper = 45.722

chi-square lower = 18.307

[(31 - 1) * 2350 / 45.722, (31 - 1) * 2350 / 18.307] = [1615.46, 4123.82]

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The area of the rectangle is 48 in².

The area of the triangle is 24 in².

The area of the triangle is half the area of the rectangle.

To calculate the area of a rectangle, we multiply the length of the rectangle by its width. And to calculate the area of a triangle we multiply the base of the triangle to the height of the triangle and divide by 2.

To calculate the area of the rectangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute into equation 1

Also, the area of the triangle is given by the formula below

Where:

Substitute into equation 2

Hence, the area of the triangle is half the area of the rectangle.

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Answer:

To write a possible quadratic inequality, we first need to determine which quadratic function has roots at x = -0.5 and x = 1.5.

We know that the solution to the quadratic inequality is x < -0.5 or x > 1.5, which means that the parabola associated with our quadratic function should not intersect the x-axis between x = -0.5 and x = 1.5.

One quadratic function with roots at x = -0.5 and x = 1.5 is:

(x + 0.5)(x - 1.5) ≤ 0

To see why this is the case, we can use a graphing calculator to graph the quadratic function y = (x + 0.5)(x - 1.5) and observe that the function is negative (i.e., has a y-value less than zero) when x is less than -0.5 or greater than 1.5.

Alternatively, we can use the fact that the product of two factors is less than or equal to zero if and only if one factor is positive and the other is negative.

Since (x + 0.5) is positive for x > -0.5 and negative for x < -0.5, and (x - 1.5) is positive for x > 1.5 and negative for x < 1.5, the inequality (x + 0.5)(x - 1.5) ≤ 0 is true for x < -0.5 or x > 1.5, but false for -0.5 < x < 1.5.

Therefore, a possible quadratic inequality that satisfies the given set of values for x is:

(x + 0.5)(x - 1.5) ≤ 0

It is possible that there is right-sided dominance in kissing behavior, based on the reported study. The fact that in a random sample of 127 kissing couples, both people in 79 of the couples tended to lean more to the right than to the left suggests a pattern of right-sided dominance.

However, it is important to note that this study alone is not conclusive evidence of right-sided dominance in kissing behavior.

Further research would be needed to confirm whether there is a consistent pattern of right-sided dominance in kissing behavior across different populations and cultures. It is also possible that other factors, such as social or psychological factors, could influence the direction in which people lean during a kiss. Therefore, it is important to approach this topic with caution and not draw any firm conclusions based on a single study.

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Answer:

I believe it's 148.

Step-by-step explanation:

You must do L x W x H to find the volume of a rectangular prism or cube.

Answer:

68 3/4 yds

Step-by-step explanation:

trust me :)

Answer:

see below

Step-by-step explanation:

area of triangle formula  = 1/2 base * height

so 1/2*6*22 =66

not sure why there's no choice of 66

Identify the predictor and response variables, then create a scatterplot in Minitab. Characterize the association between the variables as linear or nonlinear and negative, none, or positive.

In exploratory data analysis, the first step is to identify the research question and the two variables of interest. The predictor variable (also known as the explanatory variable or independent variable) is the one that is used to explain or predict the outcome of the response variable (also known as the dependent variable).

After identifying the two variables, one can use software such as Minitab to create a scatterplot of the data. The scatterplot helps to visualize the relationship between the two variables.

To characterize the association between the two variables, we would first determine if the relationship appears to be linear or nonlinear. If the relationship is roughly linear, we would then determine if it is negative (meaning that as one variable increases, the other tends to decrease), positive (meaning that as one variable increases, the other tends to increase), or none (meaning that there is no clear trend).

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Answer:

22.2

Step-by-step explanation:

Answer:

3.6 can go into 80 22 times.

Step-by-step explanation:

Answer:

$78

Step-by-step explanation:

60+30% = 78

...................

The given linear equation in slope intercept form is y = -1/4(x) - 2/7.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

By making "y" the subject of formula, we have the following:

1/4x + y = -2/7

y = -1/4(x) - 2/7

By comparison, we have the following:

Slope, m = -1/4.

y-intercept, c = -2/7.

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Answer:

Step-by-step explanation:

Hopefully this is right.

Area = (pi)r²

Which is pi times the the radius squared

The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.

Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6

My math teacher back in 7th grade gave us this sentence to help us memorize the equations.

Cherry Pie Delicious (C=(pi)d), Apple Pie Are Too (A=(pi)r²)

Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1

Question three do the same as well, and the answer will be 660.185, rounded will be 660.2

Hope this helps!