Answer:
[tex]x=\dfrac{\log 6}{\log 23}[/tex]
Step-by-step explanation:
Given exponential equation:
[tex]23^x=6[/tex]
[tex]\textsf{Apply the log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies\log_{23}6=x[/tex]
[tex]\textsf{Given change of base formula}: \quad \log_by=\dfrac{\log y}{\log b}}[/tex]
Apply the given change of base formula:
[tex]\implies x=\dfrac{\log 6}{\log 23}[/tex]
Past data indicate that the amount of money contributed by the working residents of a large city to a volunteer rescue squad is a normal random variable with a standard deviation of $1.40. It has been suggested that the contributions to the rescue squad from just the employees of the sanitation department are much more variable. If the contributions of a random sample of 12 employees from the sanitation department have a standard deviation of $1.75, can we conclude at the 0.01 level of significance that the standard deviation of the contributions of all sanitation workers is greater than that of all workers living in the city?
Answer:
We fail to reject the Null and conclude that the standard deviation of the contributions of all sanitation workers is not greater than that of all workers living in the city.
Step-by-step explanation:
σ = 1.40 ; σ² = 1.40² = 1.96
H0 : σ² = 1.96
H0 : σ² > 1.96
Given that:
Sample size, n = 12
Population Standard deviation, σ = 1.40
Sample standard deviation, s = 1.75
α = 0.01
The test statistic :
χ² = [(n-1)s²] ÷ σ²
χ² = [(12 - 1) * 1.75²] ÷ 1.40²
χ² = (11 * 3.0625) ÷ 1.96
χ² = 33.6875 / 1.96
χ² = 17.1875
χ² = 17.19
Using the Pvalue from Chisquare score calculator;
df = n - 1 ; 12 - 1 = 11
Pvalue ; χ²(17.19, 11) = 0.10238
Since Pvalue > α ; We fail to reject the Null and conclude that the standard deviation of the contributions of all sanitation workers is not greater than that of all workers living in the city.
To get to his parents' house, Dylan would have to drive due north 8 miles. To get to his
grandparents' house, he would have to drive due east 5 miles. What is the straight-line
distance between the parents' and grandparents' houses? If necessary, round to the nearest
tenth.
When Dylan travels 8 miles due north, the distance between the homes of the parents and grandparents is thus 9 miles.
what is pythagoras theorem ?The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides. With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares. The base for more intricate trigonometry ideas, such as the Pythagorean theorem's opposite, is provided by this theorem, which is a very helpful tool.
given
by pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\c^{2} = 8^{2} + 5^{2} \\c^{2} = 64 + 25 \\c^{2} = 89 \\c = 9[/tex]
The homes of the parents and grandparents are thus 9 miles apart in a straight line.
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Witch ones do I select
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
U/5 = 17/11
U = 17/11 X 5
U = 7.72
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For the 1996 General Social Survey, conducted by the National Opinion Research Center NORC, 842 replied "yes" and 982 replied "no. " Let π denote the population proportion who would reply "yes. " Find the P-value for testing H0 : π = 0. 5 using the score test, and construct a 95% confidence interval for π. Interpret the results
At a significance level of 0.05, the sample data is not consistent with the null hypothesis that the proportion of population who would respond "yes" is 0.5. The P-value of 0.0005 is less than 0.05, and also the sample proportion 0.4616 is not in the interval (0.477, 0.523) which we found as 95% Confidence interval.
Therefore, we reject the null hypothesis and conclude that the population proportion of "yes" responses is different from 0.5.
The P-value for a score test for H0: π = 0.5 can be found using the z-score and a standard normal table. The z-score is calculated as
[tex]z = \frac{x-0.5}{0.5\sqrt{\frac{x-0.5}{n} } }[/tex], that is
z = (x - 0.5) / (√(0.5(1 - 0.5) / n)
where x is the sample proportion of "yes" responses (842 / (842 + 982) = 0.4616), π is the population proportion of "yes" responses, and n is the sample size (842 + 982 = 1824).
[tex]z = \frac{0.4616-0.5}{0.5\sqrt{\frac{0.4616-0.5}{1824} } }[/tex]
= (0.4616 - 0.5)/ (√(0.5(1 - 0.5) / 1824)
This gives a z-score of -3.28.
To find the P-value, we can use the standard normal table to find the probability of observing a z-score less than -3.28. This P-value is approximately 0.0005, which is less than the commonly used significance level of 0.05. Therefore, we would reject the null hypothesis that π = 0.5.
To construct a 95% confidence interval for π, we can use the formula for a normal approximation interval:
π ± z×(√(π(1-π) / n)) that is
[tex]\pi \frac{+}{} z\frac{\pi (1 -\pi )}{n}[/tex]
Where π = 0.5, z = 1.96 (for a 95% confidence level), and n = 1824.
This gives a 95% confidence interval of (0.477, 0.523)
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Help me pleaseee!!!!
Answer:
y = (10 + 7)/x or y = x/10 + 7/10
Step-by-step explanation:
y = 10x - 7
switch x and y
x = 10y - 7
add 7 to both sides
x + 7 = 10y
Divide both sides by 10
(x + 7)/10 = y
Flip
y = (10 + 7)/x or y = x/10 + 7/10
Mars has an angular size of approximately 8. 0 arcseconds as is 175,000,000 km away. Use S = r x a to figure out the diameter of Mars
The diameter of Mars is 6825 kilometers.
First we quantify angular size a = 8. 0 arcseconds in radians.
a = ( 8/ 3600) × (π/180)
a = 0.000039 radians
also, the distance from Earth to Mars in kilometres is 175,000,000 km
So, r = 175,000,000 km
We use the formula S = r x a to find the diameter of Mars
Substitute r = 175,000,000 and a = 0.000039 in above formula
S = 175,000,000 × 0.000039
S = 6825 km
Therefore, the diameter is 6825 km
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5. Write two expressions for the area of the big rectangle.
Answer:
Two expressions for the area are;
i) x/3 + 2·y + 6
ii) (1/3) × (x + 6·y + 18)
Step-by-step explanation:
The given dimension of the rectangle are;
The height of the rectangle, h = 1/3
The width of the smallest rectangle, w₁ = x
The width of the med sized rectangle, w₂ = 6·y
The width the large rectangle, w₃ = 18
The area, 'A', of the entire rectangular figure, the big rectangle, can be expressed as follows;
A = A₁ + A₂ + A₃
Where;
A₁ = The area of the smallest rectangle
A₂ = The area of the mid sized rectangle
A₃ = The area of the large rectangle
∴ A = (1/3) × x + (1/3) × 6·y + (1/3) × 18 = x/3 + 2·y + 6
The area of the big rectangle. 'A', can also be found as follows;
A = (1/3) × (x + 6·y + 18)
Therefore, two expressions for the area of the big rectangle are;
x/3 + 2·y + 6 and (1/3) × (x + 6·y + 18).
Question 12(Multiple Choice Worth 4 points) (02.01 LC) Which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country? Simple random sampling, because the people in the sample are accessible and available Stratified sampling, because there are specific subgroups to investigate Systematic sampling, because of the ease in selecting every nth person Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement All the above sampling methods
The option 1 "Simple random sampling, because the people in the sample are accessible and available" is correct for the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.
In the given question, we have to find which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.
As we know that, you must carefully consider how you will choose a sample that is representative of the group as a whole if you want to make accurate conclusions from your data. It is known as a sampling method.
Every individual in the population has an equal chance of being chosen in a simple random sample. The entire population should be included in your sampling frame.
You might utilize instruments like random number generators or other methods that just rely on chance to carry out this kind of sampling.
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The complete question is:
Which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country?
(1) Simple random sampling, because the people in the sample are accessible and available
(2) Stratified sampling, because there are specific subgroups to investigate
(3) Systematic sampling, because of the ease in selecting every nth person
(4) Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement
(5) All the above sampling methods
I need help plz look at picture thx
The answer is G. N=2 (75) d
Can the sine ratio of an acute angle be greater than 1?
No, the sine ratio of an acute angle cannot be greater than 1. The sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio will always be less than one.
To what does sin equate?
In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.
It's important to note that if you were to give an angle value greater than 90 degrees, the sine of the angle will be a negative value, but the ratio will still be less than one.
The sine ratio is a value between -1 and 1, and it is impossible for the sine of an acute angle to be greater than 1.
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How do you factor 10^2 + 9x - 7
Step-by-step explanation:
10²+9x-7
BRAINILIEST PLEASEI neeed answers plz for the whole page
Answer:
d
50.5
not a function
A
? cant see the last one
Step-by-step explanation:
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
Explain what the ratio 5:73 represents.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 5:73 represents the ratio of 7th grade football players to total athletes.
The ratio 5:73 represents the ratio of total athletes to 7th grade football players.
The ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.
What is a ratio?A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.
What does the ratio 5:73 mean?5 : This is the number of baseball players who are in 8th-grade
73: This is the total of players. You get this number if you add all the numbers given.
Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".
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write the equation of the cirlce, in standard form which has endpoints of a diameter at (-5,-5) and (7,2)
The equation of the circle in standard form is ( x-h )2 + ( y-k)2 = r2. we can get the equation by putting the values of x coordinates and y coordinates of the circle.
A circle can be defined as a 2-D closed geometrical shape whose boundary points are at an equal distance from the center of the geometry.
Equation of the circle in standard form is,
( x-h )2 + ( y-k)2 = r2
we have to find the the x-coordinate (h) & y-coordinate (k) of the center of the circle by taking the summation of x-coordinates & y-coordinates of the endpoints of the diameter respectively and dividing by 2.
here, h = ( x1 + x2 ) / 2
k = ( y1 + y2 ) / 2
here endpoints of a diameter are at (-5,-5) and (7,2). Calculate the distance between (-5,-5) and (7,2) using the distance formula and divide by 2 to get the circle's radius. Substitute the center coordinates and radius into a standard form to get the equation of the circle.
so, h = -5 + 7 / 2 = 1
k = -5 + 2 / 2 = -3/2
Putting all the values we get the equation of circle in standard form.
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10 cm
3 cm
I need help with this
Answer:
Step-by-step explanation:
Dennis made an extra 245. 00 do for selling furniture was 7% of the total value of the furniture he sold. What was the total value of the furniture Dennise sold?
The total value of the furniture that was sold by Dennis is 3,500 dollars.
What is the percentage?
The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Dennis made an extra $245.00 for selling furniture.
Let the cost of the furniture be x.
Let the total value of the furniture be x + 245.
The extra $245.00 was 7% of the total value of the furniture he sold.
0.07(x + 245) = 245
x+ 245 = 3500
x = 3255
Then the total value of the furniture is (3,255 + 245 =) $3,500.
Hope it helped!
The scattered plot below shows the relationship between the total calories a meal has and the number of calories from fat.
If a meal has 300 calories from fat, how many total calories would you expect it to have?
Total 400 calories is expected to have a meal has 300 calories from fat the relationship between the total calories a meal has and the number of calories from fat .
what is scatterplot ?A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they can display the degree of connection, if any, between values of observable quantities or events (called variables). There are points on a scatter (XY) plot that depict the connection between two sets of data. The sample illustrates the weight and height of one person for each dot. Data points are plotted on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another. The values of the columns selected on the X and Y axes determine where each row in the data table is represented by a marker, whose position.
given
300 calories from fat
total = 100 + 100 + 200
= 400 calories
Total 400 calories is expected to have a meal has 300 calories from fat the relationship between the total calories a meal has and the number of calories from fat .
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If Matrix A is 5 x 2 and Matrix B is 3 x 5, then Matrix BA is 5 x 5.
Answer:
Correct, 25.
Step-by-step explanation:
A high school has a population of 2035 students and is increasing by 3% each year.
Write an exponential function to model the student population in terms of the number of years from now.
Answer:
Y=7x+67
Step-by-step explanation:
I have 2 bags of onion bhajis, one of which holds 42 bhajis. I empty them
onto a plate, making 50 bhajis. How many bhajis were in the second bag?
There were 8 bhajis in the second bag if he have 2 bags of onion bhajis, one of which holds 42 bhajis.
What is an equation ?
In mathematics, an equation is a statement that asserts the equality of two expressions, typically containing one or more variables. Equations are often written in the form of "expression = expression" or "expression - expression = 0"
Let's call the number of bhajis in the second bag "x".
We know that he total number of bhajis after emptying both bags onto the plate is 50.
So we can write an equation:
42 + x = 50
To solve for x, we can subtract 42 from both sides:
x = 50 - 42
x = 8
Therefore, there were 8 bhajis in the second bag.
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2log 6- log 12 + log 16
Answer:
[tex] log48[/tex]
Step-by-step explanation:
[tex]2log6 - log12 + log16 \\ \\ = log {6}^{2} - log12 + log16 \\ \\ = log36 - log12 + log16 \\ \\ = log \frac{36}{12} + log16 \\ \\ = log3 + log16 \\ \\ = log(3 \times 16) \\ \\ = log48[/tex]
Help me please I will mark brainiest if you give me the right answer
Answer:
Well the area is 28.27
Step-by-step explanation:
The question is unfinished ¯\_(ツ)_/¯
Answer:
36π [tex]in^{3}[/tex]
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex] = 9π
[tex]r^{2} = 9[/tex]
r = 3 = radius of the sphere
V = [tex]\frac{4\pi r^{3} }{3}[/tex] = [tex]\frac{4\pi 3^{3} }{3} = \frac{4\pi *27}{3}[/tex]
= 36π [tex]in^{3}[/tex]
Find the volume of given solid figure.
Answer:
48cm3
Step-by-step explanation:
Volume of a rectangular box = a.b.c
The volume of the solid figure: (2.2.5) + (7.2.2) = 20 + 28 = 48 cm3
Find the m∠r and m∠y
r = 88.5
y = 3/4
Step-by-step explanation:
From the lower triangle,
97 - 2x = 4x -2
Collecting all similar terms, we get
6x = 99 or x = 16.5
From the upper triangle, we can see that
5x + 6 = r ---> 5(16.5) + 6 = r or r = 88.5
Since the sum of all the interior angles of a triangle is equal to 180, we can write
4y + (5x + 6) + r = 180 ---> 4y + 5(16.5) + 6 + 88.5 = 180
4y = 3 or y = 3/4
Help quickly this is for a final!
The polygons are similar.
The perimeter of pentagon RSTPQ is ___ units.
Answer:
unidentified
Step-by-step explanation:
could you please send the other polygon or send an attachment of the whole question because this information is not enough
If the value of the discriminant is 10, then a quadratic equation has how many roots? 1) zero roots 2) one root 3) two roots 4) three roots
Please help me NO LINKS PLEASEE
Answer:
(-1, -5)
Step-by-step explanation:
going to the left makes you go into the (-, +) plane and going down from there makes you go into the (-, -) plane.
A nail salon raises their price for nails from $25 to $30. What is the percent increase?
Answer:
17%
Step-by-step explanation:
5 out of 30 is 17%
5/30 = 5 ÷ 30 = .16. rounds to .17 =17%
How many ways can we put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together
On solving the provided question, we can say that the permutation will bw , N = (4!)(5!)(3!)(3!)= 103,680
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.
we can put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together will be , N = (4!)(5!)(3!)(3!)= 103,680
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What does ln () do in Excel?
ln() is a function in Excel that calculates the natural logarithm of a number. The natural logarithm is the logarithm to the base e, where e is an irrational number approximately equal to 2.718281828.
1. Enter the number for which you want to calculate the natural logarithm in a cell.
2. Click on the cell and enter "=ln()" function (without the quotation marks) in the formula bar.
3. Within the parentheses, enter the cell reference or the number for which you want to calculate the natural logarithm.
4. Press the Enter key and the natural logarithm of the number will be calculated and displayed in the cell.
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