A convex polyhedron have 241 space diagonals.
As we know that the every pair of vertices of the convex polyhedron determines either an edge, a face diagonal or a space diagonal.
Here, we have 26 vertices.
so, the total line segments determined by the vertices:
²⁶C₂
= 26! / 2! × (26 - 2)!
= 325
Out of 325 line segments, 60 are edges (Given).
We know that each triangular face has zero face diagonals and each quadrilateral face has two face diagonals.
So there are 2 × 12 = 24 face diagonals.
This means, 325 - 60 - 24 = 241 line segments segments must be the space diagonals.
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log₂ 3+ log₂ (x-4)= 4
Answer:
In Explanation
Step-by-step explanation:
To solve for x in the equation log₂ 3+ log₂ (x-4)= 4, we can first use the logarithm identity: log₂ a + log₂ b = log₂ (ab)
So, we can rewrite the equation as:
log₂ (3(x-4)) = 4
Then we can use the definition of logarithm to find the value of x:
2^4 = (3(x-4)) = 3x-12
16 = 3x - 12
28 = 3x
x = 9 + 4 = 9
Therefore, x = 9 is the solution of the equation log₂ 3+ log₂ (x-4)= 4
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2 of 4
Workers in an office of 40 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away
Pizza
Curry
Fish & chips
Kebab
Other
Work out the size of each angle to draw a pie chart.
Od
a=
b 0
C=
Frequency
5
4
10
12
9
e=
Angle
a
b
C
d
el
The size of each angle to draw the pie chart is given as follows:
Angle a: 45º.Angle b: 36º.Angle c: 90º.Angle d: 108º.Angle e: 81º.How to obtain the size of each angle?The size of each angle in this problem is found applying the proportions.
First we obtain the relative frequency of each item, dividing the absolute frequency by 40.
Then we obtain the angle size, multiplying the relative frequency by 360º, which is the angle measure of the entire circumference of the pie chart.
Then the angle measures are obtained as follows:
Angle a: 5/40 x 360 = 45º.Angle b: 4/40 x 360 = 36º.Angle c: 10/40 x 360 = 90º.Angle d: 12/40 x 360 = 108º.Angle e: 9/40 x 360 = 81º.More can be learned about proportions at https://brainly.com/question/24372153
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Can someone help with problem 1 and 2
To find the sum of interior angles of a polygon, multiply the number of triangles formed inside the polygon to 180 degrees.
How to find the sum of interior angles ?
The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.Each interior angle of a regular hexagon has a measure of 120°. Because the sum of these angles will always be 360°, then each exterior angle would be 60° (360° ÷ 6 = 60°). If each exterior angle is 60°, then each interior angle is 120° (180° − 60° = 120°).The angles that lie inside a shape, are said to be interior angles, or the angles that lie in the area bounded between two parallel lines that are intersected by a transversal are also called interior angles.
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Fraction A pet store that sells birds has 12 male birds for every day 9 female birds write the ratio of female birds
The ratio of female birds is 3/7.
Explain ratio.One way to express something as a percentage of another is to use a ratio, which is a mathematical concept.
How are ratios determined?By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B). You are multiplying information A by information B, as indicated by this. For instance, if A is 5 and B is 10, your ratio will be 5/10.
The pet store has 12 male birds for every 9 female birds.
total birds = 12 + 9 = 21 birds.
So, the ratio of female birds = female birds / total birds
= 9/21
= 3/7
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What is the length of every median in an equilateral triangle whose side length is 5?
Answer:
√18.75 ≈ 4.33
Step-by-step explanation:
The median joins a vertex and the opposite side's midpoint.
side = 5
half side = 2.5
a² + b² = c²
2.5² + b² = 5²
b² = 18.75
b = √18.75
b = 4.33
The length of every median in an equilateral triangle whose side length is 5 is 4.330127018922193.
An equilateral triangle is one in which the angles and all three sides are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees. Due to its equal sides and angles, the equilateral triangle is regarded as a regular polygon or triangle.
In an equilateral triangle, all three medians have the same length.
The length of a median in an equilateral triangle can be found using the formula:
median length = (side length * sqrt(3))/2.
Therefore, in an equilateral triangle with a side length of 5, the length of each median would be,
[tex]=5*\sqrt{3}/2 \\=2.5*\sqrt{3}\\= 4.330127018922193[/tex].
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In a multicellular organism such as a dog or cat which structures listed would present the greatest in number?
In a multicellular organism such as a dog or cat have tens of trillions of cells and 60 to 80 million cells respectively. So we can say that dog have greatest number of cells
Organisms with many cell types and specialized cells that are gathered together to perform specific duties are known as multicellular organisms. An example of a multicellular organism with organization is a tree or a cat, which have tissues, organs, and organ systems.
Although we are unsure of the actual number of cells in a typical dog, we can estimate it roughly. We may apply this number to dogs, which have in the tens of trillions of cells, as some sources give a ballpark estimate of about fifty trillion cells within a human body. 60 to 80 million cells make up a cat.
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I really need help on this!
3. What are the three inequalities which define the in shaded region
The three inequalities that define the shaded region are given as follows:
y < 2.y > 2x.y ≤ -x - 2.How to define the inequalities?The inequality that defines the values below the vertical line y = 2 is given as follows:
y < 2.
(open interval as the line is dashed).
The increasing line has an intercept of 0 and slope of 2, with values to the right being shaded and the line being dashed, hence the inequality is given as follows:
y > 2x.
The decreasing line has an intercept of -2 and a slope of -1, with values to the left being shaded, with a closed interval, as the line is shaded, hence the inequality is given as follows:
y ≤ -x - 2.
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an insured has chosen joint and 2/3 survivor as the settlement option. what does this mean to the beneficiaries?
Joint and 2/3 survivor means that if the insured passes away, two of the beneficiaries will receive two-thirds of the insurance benefits, and the remaining third will be divided among all three beneficiaries.
Understanding Joint and 2/3 Survivor Settlement OptionJoint and 2/3 survivor is a settlement option for life insurance policies which means that when the insured passes away, two of the beneficiaries will receive two-thirds of the death benefits, while the remaining third will be divided equally among all three beneficiaries. This is beneficial because it ensures that two of the beneficiaries will receive the majority of the death benefits, while the remaining third will be split equally among all three. This provides a more secure financial future for the two beneficiaries receiving the most money as well as allowing the remaining third to be split equally, providing more financial security for all beneficiaries.
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The first three terms of a sequence are given. Round to the nearest thousandth
[tex]2~~,~~\stackrel{2\cdot \frac{5}{2}}{5}~~\stackrel{5\cdot \frac{5}{2}}{\cfrac{25}{2}}~~,~~...\hspace{5em}\stackrel{\textit{common ratio}}{r=\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=2\\ n=9\\ r=\frac{5}{2} \end{cases}[/tex]
[tex]a_9=2\left( \frac{5}{2} \right)^{9-1}\implies a_9=2\left( \frac{5}{2} \right)^8\implies a_9=2\left( \cfrac{390625}{256} \right) \\\\\\ a_9=\cfrac{390625}{128}\implies {\Large \begin{array}{llll} a_9=3051\frac{97}{128} \end{array}}[/tex]
In the last three years, Frederico's basketball team won 50 more games than they lost. If they won 140 games, what was the ratio of wins to losses? Write the ratio in all three forms.
Answer:
Step-by-step explanation:
won 140
lost 140-50=90
Ratio wins to losses: 14:9
Jeff wants to purchase a television for his first apartmentThe television costs 750. He can get a zerointerest loan for the television if he pays $100 per month. At the same time, he puts away $200 per month in savings. To figure out when his savings will equal the remaining amount he owes on the television , he starts writing a system of equations :
The correct equation for Jeff after every cost will be y = 750 -100x
Cost of the television = $750
Loan amount paid per month = $100
Amount put in savings = $200
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Since the amount of $200 is being saved, this means that it is not going away or is being spent. Now, as per the question, the initial remaining balance with Jeff is 750. The balance decreases by the loan amount of 100 per month.
This means that the amount is reduced by = 100x.
Therefore, the equation describing the scenario is -
y = 750 -100x
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PLEASE HURRY, TEST QUESTION, LIMITED TIME!
Question- Write the standard form equation of the circle given the center of (-3, -8) and the circumference of 14π. Show all work using the equation editor to calculate the missing pieces of the equation.
Answer: (x + 3)^2 + (y + 8)^2 = 14pi^2
(x-h)^2 + (y-k)^2 = r^2
*
The endpoints of AB are A(-7, 0) and B(7, 7).Find the coordinates of the midpoint M.
Step-by-step explanation:
( x1 + x2 /2 , y1 + y2 / 2 )
= ( -7 + 7 / 2 , 0 + 7 / 2 )
= ( 0, 3.5 )
Lance and 7 other friends go to an activity center together. They each pay $5. 95 for dinner, 84 for laser tag, $3. 60 for bowling
shoes, and $2. 25 for video games. The total amount they spent is 8 (5. 95) +8 (4) +8 (3. 60) +8 (2. 25).
Part A
Rewrite the expression so that it only has one multiplication operation
Enter the correct answer in the box
The correct expression that will form with one multiplication operation is 8 × (5.95 + 84 + 3.60 + 2.25).
Firstly rewriting the correct expression according to the amount spent by each person on different entities. The expression will be -
Total amount spent by 8 people = number of people × (amount spent on dinner + laser tag + bowling shoes + video games)
Now keeping the values in formula to find the total amount spent by eight people in desired format.
Total amount spent by eight people = 8 × (5.95 + 84 + 3.60 + 2.25)
Performing addition to simplify the expression is -
Total amount spent by eight people = 8 × 95.8
Thus, the correct simplified expression will be 8×95.8.
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Steve is constructing a
triangle from scrap wood.
He has one piece that is
20 inches and a second
piece that is 15 inches
When he is looking for
a third piece, what range
of sizes should he try
to find?
Answer:
Step-by-step explanation:
the new one will tell you be
What are the answers they are due next period
Helppp
Answer:A.½ B.-½ C.2⁷/20
Step-by-step explanation:A. 5¾+(-¼) =23/4 - ¼ =22/
=5½
B. -⅔+⅙ = (-4+1)/6=-½
C. -8/5-¾= (-32-15)/20 =47/20 =2⁷/
I need help im begging yall to help the question is which graph represents the solution to the given system y=-3x-4 and y+4-3x? A. infinit many solutions B no solutions C.(0.-4) D.(0,4) im in the last test of the semester
Answer:
D is the one trust me man I do this all the time and good luck on your exam
what is the solution to the inequality?
The solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.
What is inequality?
An inequality is a statement that compares two expressions and asserts that one is greater or less than the other. It can be represented using mathematical symbols such as <, >, ≤, ≥, ≠.
|2x + 3| < 7 is a type of absolute value inequality. The absolute value of a number is its distance from zero on the number line, and is always positive. So, |2x + 3| is the absolute value of 2x + 3, which is always greater than or equal to zero.
To solve this inequality, we need to consider two cases:
If 2x + 3 is greater than or equal to zero, we can drop the absolute value bars and solve the inequality as is:
2x + 3 < 7
2x < 4
x < 2
If 2x + 3 is less than zero, we need to reverse the inequality sign:
-2x - 3 < 7
-2x < 10
x > -5
Hence, the solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.
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Choose the items that complete the sentence about the key features of f(x) = 8x. The y-intercept is , the asymptote is y = , and the range is y >
According to the following graph, the y intercept is 0, the asymptote is ∞ and the range is (-∞, ∞)
In math the term called graph is defined as a pictorial representation or a diagram that represents data or values in an organized manner and the points on the graph often represent the relationship between two or more things.
Here we know that the function is f(x) = 8x.
When we plot the function then we get the graph like the following.
While we looking into plotted graph, then we have identified that the y-intercept is 0.
And the horizontal asymptote is the limit as x goes to ∞.
And the range is the set of values above the horizontal asymptote (-∞, ∞).
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Brandon invested $11,000 in an account paying an interest rate of 1% compounded
quarterly. Robert invested $11,000 in an account paying an interest rate of 13/%
compounded monthly. After 20 years, how much more money would Robert have in
his account than Brandon, to the nearest dollar?
Answer: $4,914
Step-by-step explanation:
To calculate the final balance in Brandon's account, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)
where A is the final balance, P is the initial investment, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have:
P = $11,000
r = 1% = 0.01
n = 4 (because the interest is compounded quarterly)
t = 20
so, A = $11,000(1 + 0.01/4)^(4*20) = $11,000(1.0025)^80 = $22,817.20
To calculate the final balance in Robert's account, we need to use the same formula, but with different values for r, n, and t.
In this case, we have:
P = $11,000
r = 13/100 = 0.13
n = 12 (because the interest is compounded monthly)
t = 20
so, A = $11,000(1 + 0.13/12)^(12*20) = $11,000(1.01083333)^240 = $27,731.34
To find the difference in the final balances, we subtract the final balance in Brandon's account from the final balance in Robert's account:
$27,731.34 - $22,817.20 = $4,914.14
To the nearest dollar, the difference is $4,914.
Answer:391
Step-by-step explanation:
the sum of the relative frequencies for all classes will always equal group of answer choices the sample size. the number of classes. one. any value l
The sum of the relative frequencies for all classes will always equal option (C) 1 i.e. when all relative frequencies on a set of values are added it is always equal to one.
A relative frequency tells us the number of times a particular value for a data item has been perceived to occur in relation as compared to the total number of values for that set of data items.
It is calculated by dividing the absolute frequency by the total number of values for the set of data items. It is used to express proportions, ratios, percentages, etc.
Absolute frequency is a mathematical term used in statistics to calculate the number of times a value occurs in a trial set of values. It is used to calculate relative frequency, and display a graph to give a visual representation.
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621900 house cost 5.4 mortgage interest rate how  much do you have to pay monthly over 5 years
Over a period of 5 years, the amount that you would have to pay monthly is given as $3,201.37
How to solve for the mortgageTo calculate the monthly mortgage payment for a house that costs $621,900 with an interest rate of 5.4% over 5 years, you can use the following formula:
P = (r(1 + r)^n) / (((1 + r)^n) - 1) * L
Where:
P = monthly payment
r = monthly interest rate (5.4%/12 = 0.0045)
n = total number of payments (5 years x 12 = 60)
L = the loan amount ($621,900)
Plugging in the values, we get:
P = (0.0045(1 + 0.0045)^60) / (((1 + 0.0045)^60) - 1) * 621,900
P = $3,201.37
So you have to pay $3,201.37 monthly over 5 years.
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11. Angel made 1 1/3pounds of trail mix for a
hike. Is there a way Angel can break up
the trail mix into four bags? Explain.
let's firstly convert the mixed fraction to an improper fraction.
[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{trail mix}}{\cfrac{4}{3}}\div \stackrel{bags}{4}\implies \cfrac{4}{3}\div \cfrac{4}{1}\implies \cfrac{4}{3}\cdot \cfrac{1}{4}\implies \cfrac{4}{4}\cdot \cfrac{1}{3}\implies \stackrel{per~bag}{\cfrac{1}{3}}[/tex]
What is the quotient of 154,504 divided by 28 with long division?
Any ideas?
In concave equilateral pentagon ABCDE, angle A = angle B = 108 degrees. What is the degree measure of angle E?
Answer:
In an equilateral pentagon, all angles have equal degree measures, so to find the degree measure of one angle, we need to find the sum of the degree measures of the interior angles and then divide by the number of angles.
Step 1: Find the sum of the degree measures of the interior angles of the pentagon:
180 * (5 - 2) = 540 degrees
Step 2: Divide the sum by the number of angles:
540 degrees / 5 angles = 108 degrees
The degree measure of angle E is 108 degrees.
The degree measure of angle E is 108°.
We can use interior angels theorm.
The sum of the interior angles of a pentagon can be calculated using the formula:
Interior angle sum = (n - 2) × 180
where n is the number of sides of the polygon.
In this case, n = 5, so the sum of the interior angles of the pentagon is (5 - 2) × 180 = 540°.
Since angle A and angle B are both equal to 108°, we can say that:
angle A + angle B = 2 × 108 = 216°.
So, the sum of the remaining three interior angles (angles C, D, and E) is:
540 - 216 = 324°
Since each of these three angles is equal, the measure of each angle must be 324° divided by 3, or:
324 ÷ 3 = 108°
So, the degree measure of angle E is also 108°.
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(a) Draw the graph of y=x²+x-5 for values of x ranging from -4 to +3. Use a scale of 1cm to 1 unit on both axes. (b) On the same graph draw the line y = 2(x-1). From your graph: (c) find the roots of the equation x²+x-5=0 (d) deduce the roots of the equation x²+x-7=0 (e) deduce the roots of the equation x²+x-5=2(x-1) (f) state the minimum value of x2+x-5.
We must first plot the given linear equation before we can draw the graph for it. Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.
How do you deduce roots?link the points that lie on it to form a straight line.
Y = 2x - 1 is the first equation.
Calculate the corresponding values of y by substituting various values of x into the equation.
X Y = 2x-1 point (x, y)
0 -1 (0, -1)
2 3 (2, 3)
4 7 (4, 7)
-1 -3 (-1, -3)
-3 -7 (-3, -7)
On the graph paper, place these points and draw a straight line connecting them.
Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.
In order to determine the critical point, we will set the first derivative of the function to zero and solve for x. We may determine whether this point will be a maximum or minimum by taking the second derivative, or f"(x). It will be a minimal value if the second derivative is positive.
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Suppose 0 is an angle in the standard position whose terminal side is in quadrant IV and cot 0 = -9/18. Find values of five remaining trigonometric functions of 0.
The values of five remaining trigonometric functions of θ.
sinθ = 1/√5, cosθ = 2/√5, tanθ = 2, secθ = √5/2, cosecθ = √5
We have to determine values of five remaining trigonometric functions of θ. Suppose θ is an angle in the standard position whose terminal side is in quadrant IV and cot θ = -9/18.
The ratio of trigonometry is:
sinθ = Perpendicular/Hypotenuse
cosθ = Adjacent Side/Hypotenuse
tanθ = Perpendicular/Adjacent Side
cotθ = Adjacent Side/Perpendicular
sec = Hypotenuse/Adjacent Side
cosec = Hypotenuse/Perpendicular
We know that;
Adjacent Side = 9, Perpendicular = 18
Now finding the value of Hypotenuse using the Pythagorean Theorem
(Hypotenuse)^2 = (Adjacent Side)^2 + (Perpendicular)^2
(Hypotenuse)^2 = (9)^2 + (18)^2
(Hypotenuse)^2 = 81 + 324
(Hypotenuse)^2 = 405
Taking square root on both side, we get
Hypotenuse = 9√5
Now finding the other trigonometry ratio:
sinθ = Perpendicular/Hypotenuse
sinθ = 9/9√5
sinθ = 1/√5
cosθ = Adjacent Side/Hypotenuse
cosθ = 18/9√5
cosθ = 2/√5
tanθ = Perpendicular/Adjacent Side
tanθ = 18/9
tanθ = 2
secθ = Hypotenuse/Adjacent Side
secθ = 9√5/18
secθ = √5/2
cosecθ = Hypotenuse/Perpendicular
cosecθ = 9√5/9
cosecθ = √5
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After making several scale drawings, Joseph
decides on the best placement for a new grill on
his deck. He uses a scale of 2 cm for every 5 in.
What is the actual area of the space for Joseph's
new grill in square inches?
Answer: 50
Step-by-step explanation:
i don't know how i got this but yeah its 50
a truck is moving at the rate of 50 miles per hour, and the diameter of each wheel is 3 feet. what is the angualr speed of the wheels in raidans per minute
The angular speed of the wheels is approximately 1480 / π radians per minute.
We can start by converting the velocity of the truck from miles per hour to feet per minute, since the diameter of the wheels is given in feet.
50 miles/hour = 50 x 5280 feet/hour = 264,000 feet/hour
264,000 feet/hour / 60 minutes/hour = 4,400 feet/minute
Next, we can find the circumference of the wheel and then divide it by the velocity of the truck to find the angular velocity in radians per minute:
Circumference = 2 * π * r = 2 * π * (diameter/2) = 2 * π * (3 feet / 2) = 3π feet
Angular velocity (ω) = velocity / circumference = 4,400 feet/minute / (3π feet) = 1480 / π radians/minute
So the angular speed of the wheels is approximately 1480 / π radians per minute.
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