The solution to the equation 1/3a = -15 is a = -45
How to determine the solution to the equationfrom the question, we have the following parameters that can be used in our computation:
1/3a = -15
Multiply 3 to both sides of the equation
so, we have the following representation
3 * 1/3a = -15 * 3
When the products are evalated, we have
a = -45
Hence, the solution to the equation is a = -45
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A stainless steel patio heater is a square pyramid. the length of one of the base is 23.8. The slant height of the pyramid is 89.3 in. What is the height of the pyramid?
To find the height of the square pyramid, we can use the Pythagorean theorem. The slant height of the pyramid (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height.
Using the Pythagorean theorem:
s^2 = (b/2)^2 + h^2
We are given that the length of one of the base sides (b) is 23.8 and the slant height (s) is 89.3.
Plugging in the values:
89.3^2 = (23.8/2)^2 + h^2
Simplifying:
h^2 = 89.3^2 - (23.8/2)^2
h^2 = 7950.49 - 141.64
h^2 = 7808.85
Taking the square root of both sides:
h = √7808.85
h ≈ 88.37
Therefore, the height of the square pyramid is approximately 88.37 inches.[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]
What is n^2-11n+10
Please explain step by step and detailed to get the answer
The factored expression of n² - 11n + 10 is (n - 10)(n - 1)
How to factorize the expressionFrom the question, we have the following parameters that can be used in our computation:
n² - 11n + 10
To determine the pair of factors to factor the expression, we find two expressions
That must add up to -11nThat must mutiply to 10x²using the above as a guide, we have the following:
The expressions are -10n and -n
So, we have
n² - 11n + 10 = n² - 10n - n + 10
When factored, we have
n² - 11n + 10 = (n - 10)(n - 1)
Hence, the factored expression of n² - 11n + 10 is (n - 10)(n - 1)
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
Answers following the rounding instructions: see below for details
BC = 5.1
m∠B = 23°
m∠V = 116°
Step-by-step explanation:
Givens:
AC = 3
AB = 7
m∠A = 41°
Unknowns:
BC = ?
m∠B = ?
m∠C = ?
Find side BC using the law of cosines: c² = a² + b² - 2ab cos(C)
a² = 3² + 7² - 2(3)(7)(cos41)
a = √9 + 49 - 42(cos41)
a = 5.128 ≈ 5.13
side BC = 5.13
Use the law of sines to find m∠B: sin(A) / a = sin(B) / b = sin(C) / c
m∠B = sin⁻¹[sin41/5.13 x 3] = sin⁻¹(0.3837) = 22.56 ≈ 22.6°
Sum of interior angles of a triangle is 180, so now you can find m∠C:
m∠C = 180 - 22.6 - 41 = 116.44 ≈ 116.4°
Rounding side BC to nearest tenth: BC = 5.1
Rounding angles to nearest whole degree:
m∠B = 23°
m∠V = 116°
Need the answer ASAP
Answer: A. x=3 y= -1 z=4
Step-by-step explanation:
I plugged it into my graphing calculator.
>2nd Matrix
>Edit >A
>choose 3x3
>Enter all coefficients as they look
>2nd Matrix
>Edit >B
>Choose 3x1
>Enter answers as they look
Go to main page
[tex][A]^{-1} [B]\\[/tex]
Answers end up being 3, -1, 4
Can someone help me with 12 & 13. And show your work!
Answer:
please see answers below
Step-by-step explanation:
Volume of sphere = (4/3) X π X r ³
volume of hemisphere = (2/3)X π X r ³
12) volume of hemisphere = (2/3)X π X r ³
= (2/3) X π X (5)³
= (250/3)π
= 261.80 km³ to nearest hundredth
13) 18 foot is the diameter. radius = 1/2 X diameter = 9.
volume of hemisphere = (2/3)X π X r ³
= (2/3) X π X (9) ³
= 1526.81 ft³ to nearest hundredth
100 Points! Geometry question. Photo attached. Use the Pythagorean Theorem to find x. Please show as much work as possible. Thank you!
The value of x is approximately 34.02.
Given that in a rectangle with length 31 and width is 14 and the diagonal length is x.
To find the value of x using the Pythagorean Theorem, we can consider the rectangle as a right triangle, where the length and width of the rectangle form the two sides of the triangle, and the diagonal length (x) is the hypotenuse.
According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying the given data gives,
[tex]x^2 = length^2 + width^2[/tex]
Substituting the given values into the equation:
diagonal length [tex]x^2 = 31^2 + 14^2[/tex]
diagonal length [tex]x^2[/tex] = 961 + 196
diagonal length [tex]x^2[/tex] = 1157
To find x, we take the square root of both sides:
diagonal length x = [tex]\sqrt{1157}[/tex]
diagonal length x = 34.02
Therefore, the value of x is approximately 34.02.
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a shade of paint purple berry can be made by mixing red and blue paint in the ratio 5:2. Emma has 30 litres of red paint and 10 litres of blue paint.work out the maximum volume of purple berry that can be made
Answer:The max volume of Purple berry paint is 85
Step-by-step explanation:
Purple = Red + Blue
P = 5 : 2
Simplify 5 : 2 which is 2.5 : 1
P = 30L : 10L
P = (30 x 2.5 ) + (10 x 1)
P = 75 + 10
P = 85 L
A sample of 22 observations selected from a normally distributed population produced a sample variance of 18 . a. To see if the population variance differs from 14 write the null and alternative hypotheses. b. Using �=.05α=.05, find the critical values of �2χ2. Display the chi-square distribution curve's rejection and nonrejection areas. c. Determine the test statistic �2χ2 value. d. Will you reject the null hypothesis presented in component an at a 5% significance level?
The degrees of freedom is 21, the critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas and chi-square test statistic is 27.
The null and alternative hypotheses can be stated as follows:
Null Hypothesis (H0): The population variance is equal to 14.
Alternative Hypothesis (Ha): The population variance differs from 14.
To find the critical values of χ2 with α = 0.05, we need to determine the degrees of freedom first.
For a sample variance, the degrees of freedom (df) is given by (n - 1), where n is the sample size.
In this case, n = 22, so the degrees of freedom is 21.
Using a chi-square table or statistical software, we can find the critical values for a chi-square distribution with 21 degrees of freedom and α = 0.05.
The critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas.
To determine the test statistic χ2 value, we need to calculate the chi-square test statistic using the given information.
The chi-square test statistic is calculated as:
χ2 = (n - 1) ×(sample variance) / (population variance)
Plugging in the values, we have:
χ2 = (22 - 1) × 18 / 14
=27
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b. Does there appear to be any relationship between these two variables?
a. colder average low-temperature seems to lead to higher amounts of snowfall
b. there is no relationship
c. colder average low-temperature seems to lead to lower amounts of snowfall
c. Based on the scatter diagram, comment on any data points that seem to be unusual.
an average snowfall of nearly 100 inches.
a. no city has
b. only one city has
c. two cities have
d. three cities have
e. four cities have
f. more than four cities have
1. There is no relationship
2. Two cities have an average snowfall of nearly 100 inches.
What is the scatter plot?
A scatter plot, also known as a scatter diagram or scatter graph, displays the relationship between two variables. It is particularly beneficial for identifying any patterns or trends in the data and showing how one variable might be related to another.
In a scatter plot, each data point is represented on the graph by a dot or marker. The horizontal axis (x-axis) is frequently used to represent the independent variable or predictor, while the vertical axis (y-axis) is frequently used to represent the dependent variable or reaction. Each dot's locations on the graph correspond to the values of the two variables for that particular data point.
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Find the area of the following rectangle. a = 12 ft b = 14 ft A = ft 2
Answer:
The area of the rectangle is 168 ft².
Step-by-step explanation:
Formula: A = lw
where l and w are the length and width of the rectangle respectively.
We're given with the length and the width as
a = 12 ft
b = 14 ft
Let's solve for the area using the formula above.
A = lw
A = 12ft(14ft)
A = 168 ft²
Question #3
Determine if the following scenario is best described as an observational study, survey, or experiment.
A researcher wants to determine the effects of eating a vegan diet on overall health. The researcher finds 200 individuals, where
of them have eaten vegan for the past five years and the other 100 have not eaten vegan for the past five years. The participants
each given a health assessment and the data is analyzed in order to draw conclusions about how eating vegan can affect one's
overall health.
Experimental Study
Observational study
Saved Survey
The type of sytudy that we have here is the observational study.
What is the observational study?
In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.
In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.
The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.
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100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
626.71 cm^2
Step-by-step explanation:
Area of figure = area of half circle + Area of half circle + area of a rectangle
here, diameter=15 cm
radius = 15/2=7.5 cm
length=30cm
breadth=15cm
Now
Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth
=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15
=626.71 cm^2
Solve for angles x and y in the triangle below. Round your angle to the nearest whole degree.
Solve for both x and y
[tex]\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o[/tex]
Make sure your calculator is in Degree mode.
Solve for x. Round your answers to two decimal places.
2x2 + 7x = 3
Answer:
[tex]x\approx0.39,-3.89[/tex]
Step-by-step explanation:
[tex]\displaystyle 2x^2+7x=3\\2x^2+7x-3=0\\\\x=\frac{-7\pm\sqrt{7^2-4(2)(-3)}}{2(2)}\\\\x=\frac{-7\pm\sqrt{49+24}}{4}\\\\x=\frac{-7\pm\sqrt{73}}{4}\\\\x\approx0.39,-3.89[/tex]
100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
38.9 in²
Step-by-step explanation:
You want the area of the composite figure that is an 8-inch square with a semicircle removed.
Semicircle areaThe missing semicircle has a diameter of 8 in, so a radius of 4 in. The area of that half-circle is ...
A = 1/2πr² = (π/2)(4 in)² = 8π in² ≈ 25.1 in²
Square areaThe area of the square without the semicircle removed is ...
A = s² = (8 in)² = 64 in²
Composite areaAfter removing the semicircle from the square, the remaining area is ...
A = square area - semicircle area
A = 64 in² -25.1 in² = 38.9 in²
The area of the figure is about 38.9 square inches.
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These shapes are similar.
Find X.
X
9
5
27
15
21
Answer:
15
Step-by-step explanation:
A 27 - foot ladder is leaning against the wall. If the top of the ladder touches 22.5 feet up the wall, what is the angle evaluation of the ladder
Answer:
Step-by-step explanation:
A spinner has six equal-sized sections. The sections are labeled red, blue, green, red, blue, and blue. How many outcomes are in the sample space?
The outcomes that are in the sample space are red, blue, green, red, blue, and blue.
How to determine the outcomes that are in the sample space?From the question, we have the following parameters that can be used in our computation:
Spinner = 6 sections
This means that
The spinner has 6 sections and as such, the sample size of the spinner is 6
The sample space are the colors in the spinner
So, we have
Space = red, blue, green, red, blue, and blue.
Hence, the outcomes that are in the sample space are red, blue, green, red, blue, and blue.
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helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer: $1.50 for every 1 pound
Step-by-step explanation:
If 2 pounds equal to $3.00 divide $3.00 by 2 and you end up with $1.50, you can also keep adding $1.50 to get the other prices.
Help Quickly! A truck needs 7 gallons of fuel to travel 56 miles. Can the truck travel 48 miles with 6 gallons of fuel? Explain.
Giving brainliest
Pick A, B, C, or D
how many inches is it from end to end on a bed that is 6 feet long? It is measured in the.
The calculated inches from end to end on the bed is 72 inches
How to determine the inches from end to end on the bedFrom the question, we have the following parameters that can be used in our computation:
Length = 6 feet long
By conversion of units, we have
1 feet = 12 inches
using the above as a guide, we have the following:
Length = 6 * 12 inches long
Evaluate the products
Length = 72 inches long
Hence, the inches from end to end on the bed is 72
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Pls help me with this asap
Container #1 is the only one large enough to hold the contents of a one liter bottle of soft drink.
Container #1: The volume formula for a cylinder is V = πr²h, where r is the radius and h is the height.
Radius (r) = 8 cm / 2 = 4 cm
Height (h) = 19 cm
So, V1 = π(4 cm)²(19 cm)
≈ 3032.07 cm³
Container #2:
Radius (r) = 5 cm
Height (h) = 12 cm
Using the formula:
V2 = π(5 cm)²(12 cm)
≈ 942.48 cm³
Container #3:
Diameter (d) = 12 cm
Radius (r) = 12 cm / 2 = 6 cm
Height (h) = 10 cm
V3 = π(6 cm)²(10 cm)
≈ 1130.97 cm³
Now, Comparing the volumes:
V1 ≈ 3032 cm³
V2 ≈ 942 cm³
V3 ≈ 1131 cm³
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ILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST SOMEBODY PLEASE PLEASE HELP ME IM BEGGING YOU
Answer:
B Mean: 17.5 | W Mean: 20.5 | B Mode: 15 | W Mode: 20.5 | B Mode: 14 & 15 | W Mode: 20 & 21 | B Range: 17 | W Range: 3
Step-by-step explanation:
8 minutes before 6=?
Answer:
5:52
Step-by-step explanation:
Answer: 5:52
Step-by-step explanation:
100 Points! Geometry question. Find each measure. Photo attached. Please show as much work as possible. Thank you!
Answer:
a. 73°
b. 98°
Step-by-step explanation:
In quadrilateral EFGH
∡E+∡G=180° sum of opposite angle of quadrilateral inside the circle is 180°
substituting value
11x+8+8x+1=180°
19x+9=180°
19x=180=9
19x=171
x=171/19
x=9°
similarly,
∡H+∡F=180° sum of opposite angle of quadrilateral inside the circle is 180°
substituting value
6y-4+5y-3=180°
11y-7=180°
11y=180°+7
11y=187°
y=187/11
y=17°
Now
a. m∡G=8x+1=8*9+1=73°
b. m∡H=6y-4=6*17-4=98°
Write a sine function with an amplitude of 5, a period of
Pi/8,and a midline at y = 7.
f(x) = 4sin(8x) + 5
f(x) = 5sin(16)+7
f(x) = 5sin(16x) + 4
f(x) = 4sin(8x) + 7
Answer:
[tex]\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}[/tex]
Step-by-step explanation:
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function[tex]\boxed{f(x) = A \sin (B(x + C)) + D}[/tex]
where:
A is the amplitude (height from the midline to the peak).2π/B is the period (horizontal distance between consecutive peaks).C is the phase shift (horizontal shift - positive is to the left).D is the vertical shift (y = D is the midline).Given values:
Amplitude, A = 5Period, 2π/B = π/8Phase shift, C = 0Vertical shift, D = 7Calculate the value of B:
[tex]\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16[/tex]
Substitute the values of A, B C and D into the standard formula:
[tex]f(x) = 5 \sin (16(x + 0)) + 7[/tex]
[tex]f(x) = 5 \sin (16x) + 7[/tex]
Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:
[tex]\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}[/tex]
The cafeteria lunch menu lists:
Pizza Cheese, Sausage, Pepperoni
Dessert - Pudding or Cookie
Drink-Water, Milk, Soda
How many different lunch meals can you construct from these choices?
O 18
O
O 81
03
Answer: 18
Step-by-step explanation:
Multiply number of each item possible
3*2*3=18
Jane buys p packets of plain crisps and c packets
of cheese and onion crisps. Write down an
expression for the total number of packets of
crisps Jane buys.
The expression for the total number of packets of crisps that Jane buys is given as follows:
p + c.
How to obtain the total number of packets?The amounts of packets of crisps purchased are given as follows:
p packets of plain crisps.c packets of cheese and onion crisps.The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.
Hence the expression for the total number of packets of crisps that Jane buys is given as follows:
p + c.
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find the surface area
The surface area of the cylinder is: 156π.
Here, we have,
given that,
the cylinder has:
radius = 6 in
height = 10 in
now, surface area of the cylinder is:
SA = 2πrh + πr²
here, we have,
SA = 2π *6 * 10 + π6²
= 120π + 36π
= 156π
Hence, The surface area of the cylinder is: 156π.
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Find x (circle)
(Btw I don’t know if 5.6 is correct so just ignore that)
Answer:
A. 11.2
Step-by-step explanation:
But this has nothing to do with 5.6 × 2. Erase that! Lol.
You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.
The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.
The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.
The hypotenuse is 14.
Let's do some Pythagorean Theorem.
Leg^2+ leg^2=hypotenuse^2
you know,
a^2 + b^2 = c^2
fill in what we know.
8.4^2 + b^2 = 14^2
simplify.
70.56 + b^2 = 196
subtract 70.56
b^2 = 125.44
squareroot both sides
b = 11.2